#19
Apr1507, 05:00 AM

P: n/a

Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at>
>Oh No schrieb: >> In the orthodox interpretation of quantum theory it only makes sense >>to >> talk of an observable quantity when a measurement is done. From that >> point of view the electron is sizeless. > >From that point of view, the sun (a slightly bigger quantum object) >is also sizeless if nobody looks at it. Such a point of view is >therefore useless. > The important fact of measurement is not that an observer formally does the measurement and observes the result, but that there are physical laws which can be applied in principle to deduce the result. When there is no one to observe a tree falling in a forest, we may assume that physical laws apply and that there were consequent vibrations in the air which we call sound, even if no one is there to hear them. I believe this point of view is anything but useless, because if we are to unify general relativity with quantum theory we should seek to understand what physical processes give rise to geometry. Regards  Charles Francis moderator sci.physics.foundations. substitute charles for NotI to email 


#20
Apr1507, 05:02 AM

P: n/a

In article <461E4183.2010006@univie.ac.at>,
Arnold.Neumaier@univie.ac.at says... > Oh No schrieb: > > > > In the orthodox interpretation of quantum theory it only makes sense to > > talk of an observable quantity when a measurement is done. From that > > point of view the electron is sizeless. > > From that point of view, the sun (a slightly bigger quantum object) > is also sizeless if nobody looks at it. Such a point of view is > therefore useless. In the first place, the Sun is a classical object; it creates lots of entropy, and the 'environment' is always looking at it. Questions of complementary measurements etc. have little application to the Sun. Whether you agree or not with Charles' argument, they do apply to position measurements on electrons. In the second place, the Sun differs from an electron in that it is composed of more than one particle, and the interactions of these particles define a size. The same applies to protons. Composite objects have a welldefined, if not always exact, size. An electron does not have welldefined component particles (virtual particles don't count). If an electron is in fact a loop of string or if it contains sub particles, then it has a size, but this size must be smaller than anything we have been able to measure so far. So I think the only answer to "What size is the electron?" is "Define what you mean by size."  Gerry Quinn 


#21
Apr1507, 05:02 AM

P: n/a

In article <461E4183.2010006@univie.ac.at>,
Arnold.Neumaier@univie.ac.at says... > Oh No schrieb: > > > > In the orthodox interpretation of quantum theory it only makes sense to > > talk of an observable quantity when a measurement is done. From that > > point of view the electron is sizeless. > > From that point of view, the sun (a slightly bigger quantum object) > is also sizeless if nobody looks at it. Such a point of view is > therefore useless. In the first place, the Sun is a classical object; it creates lots of entropy, and the 'environment' is always looking at it. Questions of complementary measurements etc. have little application to the Sun. Whether you agree or not with Charles' argument, they do apply to position measurements on electrons. In the second place, the Sun differs from an electron in that it is composed of more than one particle, and the interactions of these particles define a size. The same applies to protons. Composite objects have a welldefined, if not always exact, size. An electron does not have welldefined component particles (virtual particles don't count). If an electron is in fact a loop of string or if it contains sub particles, then it has a size, but this size must be smaller than anything we have been able to measure so far. So I think the only answer to "What size is the electron?" is "Define what you mean by size."  Gerry Quinn 


#22
Apr1507, 05:02 AM

P: n/a

In article <461E4183.2010006@univie.ac.at>,
Arnold.Neumaier@univie.ac.at says... > Oh No schrieb: > > > > In the orthodox interpretation of quantum theory it only makes sense to > > talk of an observable quantity when a measurement is done. From that > > point of view the electron is sizeless. > > From that point of view, the sun (a slightly bigger quantum object) > is also sizeless if nobody looks at it. Such a point of view is > therefore useless. In the first place, the Sun is a classical object; it creates lots of entropy, and the 'environment' is always looking at it. Questions of complementary measurements etc. have little application to the Sun. Whether you agree or not with Charles' argument, they do apply to position measurements on electrons. In the second place, the Sun differs from an electron in that it is composed of more than one particle, and the interactions of these particles define a size. The same applies to protons. Composite objects have a welldefined, if not always exact, size. An electron does not have welldefined component particles (virtual particles don't count). If an electron is in fact a loop of string or if it contains sub particles, then it has a size, but this size must be smaller than anything we have been able to measure so far. So I think the only answer to "What size is the electron?" is "Define what you mean by size."  Gerry Quinn 


#23
Apr1607, 05:00 AM

P: n/a

Gerry Quinn schrieb:
> In article <461E4183.2010006@univie.ac.at>, > Arnold.Neumaier@univie.ac.at says... >> Oh No schrieb: >>> In the orthodox interpretation of quantum theory it only makes sense to >>> talk of an observable quantity when a measurement is done. From that >>> point of view the electron is sizeless. >> From that point of view, the sun (a slightly bigger quantum object) >> is also sizeless if nobody looks at it. Such a point of view is >> therefore useless. > > In the first place, the Sun is a classical object; it creates lots of > entropy, and the 'environment' is always looking at it. Every classical object is also a quantum object, composed of myriads of quantum particles. How does it become classical? The Environment is also always looking at a single particle. Thus there is no difference. > In the second place, the Sun differs from an electron in that it is > composed of more than one particle, and the interactions of these > particles define a size. The same applies to protons. Composite > objects have a welldefined, if not always exact, size. And the same allies to electrons; their mass defines an intrinsic length scale, the Compton wavelength. > An electron does not have welldefined component particles (virtual > particles don't count). Why don't they count? The dressed stated of an electron (with a size) is made up of sizeless bare electrons, in a similar way as the hydrogen atom (with a size) is made of an electron and a proton, except that the electron invloves inifinitely many bare particles. > So I think the only answer to "What size is the electron?" is "Define > what you mean by size." It is welldefined by the literature. See my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/physicsfaq.txt (Are electrons pointlike/structureless?) Arnold Neumaier 


#24
Apr1707, 05:00 AM

P: n/a

Arnold Neumaier:
> And chemists measure the size of atoms in terms of the charge density of > their electron cloud, which is statedependent. > > So make your choice and know that others may have chosen differently. > > I prefer the choice which gives the best intuition about the behavior > of the object, and that is the statedependent size in terms of > densities. It is completely analogous to the size of a soap bubble, > which depends on its state. No, a soap bubble is made of many particles, which have a position each. The size is then defined as the distance between two somehow specified particles. An atom is made of at least two particles, so the same definition applies, even if fuzzy. If there's only one particle, you are out of luck. A wave function doesn't give several positions, there is only one, that is unknown. GML 


#25
Apr1807, 05:00 AM

P: n/a

Greg McLac schrieb:
> Arnold Neumaier: >> And chemists measure the size of atoms in terms of the charge density of >> their electron cloud, which is statedependent. >> >> So make your choice and know that others may have chosen differently. >> >> I prefer the choice which gives the best intuition about the behavior >> of the object, and that is the statedependent size in terms of >> densities. It is completely analogous to the size of a soap bubble, >> which depends on its state. > > No, a soap bubble is made of many particles, which have a position each. > The size is then defined as the distance between two somehow specified > particles. Of particles which don't have a welldefined position and hence not a welldefined distance??? > An atom is made of at least two particles, so the same > definition applies, even if fuzzy. And this size is obviously statedependent, since it depends on where these particles may be. The only stateindependent properties of an atom are the quantum numbers of its constituents and the spectrum of its Hamiltonian... You cannot maintain consistently that an atom has a size which is stateindependent. > If there's only one particle, you are > out of luck. A wave function doesn't give several positions, there is only > one, that is unknown. As the sun, a soap bubble, or an atom, a wave function has a charge density and mass density, which define lengths scales. If you measure the size of an atom by its mass density (relevant for the scattering of Xrays), the size is that commonly called the size of the nucleus. If you measure it by its charge density (relevant for chemistry), the size is that commonly called the size of the atom. These are the conventional sizes in common usage by phycisists and chemists. Arnold Neumaier 


#26
Apr1807, 05:00 AM

P: n/a

In article <4622065F.6030408@univie.ac.at>,
Arnold.Neumaier@univie.ac.at says... > Gerry Quinn schrieb: > > In article <461E4183.2010006@univie.ac.at>, > > Arnold.Neumaier@univie.ac.at says... > > > > In the first place, the Sun is a classical object; it creates lots of > > entropy, and the 'environment' is always looking at it. > > Every classical object is also a quantum object, composed of myriads > of quantum particles. How does it become classical? When it's not useful to look at it as a quantum object. Which is nearly always, in the case of an object as massive as the Sun. > The Environment is also always looking at a single particle. > Thus there is no difference. So how do we carry out experiments involving quantum phenomena? The answer is by *not* looking, over some interval of time and/or space. I also mentioned that the Sun generates entropy  effectively a continuous blizzard of measurement events. > > In the second place, the Sun differs from an electron in that it is > > composed of more than one particle, and the interactions of these > > particles define a size. The same applies to protons. Composite > > objects have a welldefined, if not always exact, size. > > And the same allies to electrons; their mass defines an intrinsic > length scale, the Compton wavelength. So it does, but to say the size of an object is given by the Compton wavelength is just silly. Apply it to the Sun, and you can see why! It may be that there are 'size' questions that can usefully be answered by referring to the Compton wavelength, but it's not a generic way of defining size. > > An electron does not have welldefined component particles (virtual > > particles don't count). > > Why don't they count? The dressed stated of an electron (with a size) > is made up of sizeless bare electrons, in a similar way as the hydrogen > atom (with a size) is made of an electron and a proton, except that > the electron invloves inifinitely many bare particles. Because they don't have any characteristic distance between them that is a function of their interactions. Atoms in the Sun, quarks in a proton, or bricks in a house do, because they are real particles. > > So I think the only answer to "What size is the electron?" is "Define > > what you mean by size." > > It is welldefined by the literature. See my theoretical physics FAQ > at http://www.mat.univie.ac.at/~neum/physicsfaq.txt > (Are electrons pointlike/structureless?) I don't believe "the size of an electron" is welldefined by the literature. For example, your web page refers to the de Broglie wavelength, and to the charge radius. Like the Compton wavelength, neither of these can be considered the obvious definition of size. By contrast, the definition for a composite object in terms of the characteric distances between its components is universal, and corresponds to ordinary concepts of 'size'. So composite particles do have a welldefined size.  Gerry Quinn 


#27
Apr1907, 05:00 AM

P: n/a

Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at>
>Greg McLac schrieb: > >> An atom is made of at least two particles, so the same >> definition applies, even if fuzzy. > >And this size is obviously statedependent, since it depends on where >these particles may be. The only stateindependent properties of an >atom are the quantum numbers of its constituents and the spectrum of >its >Hamiltonian... > >You cannot maintain consistently that an atom has a size which is >stateindependent. Normally one would assume the lowest energy eigenstate of the Hamiltonian, though you could apply the idea to any eigenstate. As Greg said, a definition applies, even if fuzzy. There is nothing wrong with the notion of the expectation of a size observable determined as relative distance between the particles. >> If there's only one particle, you are >> out of luck. A wave function doesn't give several positions, there is only >> one, that is unknown. > >As the sun, a soap bubble, or an atom, a wave function has a charge >density and mass density, which define lengths scales. It does not have a density. It has an amplitude. This is a completely different concept. Regards  Charles Francis moderator sci.physics.foundations. substitute charles for NotI to email 


#28
Apr1907, 05:00 AM

P: n/a

Gerry Quinn schrieb:
> In article <4622065F.6030408@univie.ac.at>, > Arnold.Neumaier@univie.ac.at says... >> Gerry Quinn schrieb: >>> In article <461E4183.2010006@univie.ac.at>, >>> Arnold.Neumaier@univie.ac.at says... >>> >>> In the first place, the Sun is a classical object; it creates lots of >>> entropy, and the 'environment' is always looking at it. >> Every classical object is also a quantum object, composed of myriads >> of quantum particles. How does it become classical? > > When it's not useful to look at it as a quantum object. Which is > nearly always, in the case of an object as massive as the Sun. But it remains a quantum object, even if one finds it useful to view it in a simpler approximation. >> The Environment is also always looking at a single particle. >> Thus there is no difference. > > So how do we carry out experiments involving quantum phenomena? The > answer is by *not* looking, over some interval of time and/or space. No. It is Nature who looks, and nature cannot help looking, unless the lack of interaction forbids it to look. > I also mentioned that the Sun generates entropy  effectively a > continuous blizzard of measurement events. No. Not the sun generates the entropy, but the approximate description of the sun that discards all the quantum degrees of freedom. On the fundasmental level, where the universe is a single quantum field, there is no entropy. The latter only appears through approximations, as you can learn from any statistical mechanics textbook. >>> In the second place, the Sun differs from an electron in that it is >>> composed of more than one particle, and the interactions of these >>> particles define a size. The same applies to protons. Composite >>> objects have a welldefined, if not always exact, size. >> And the same allies to electrons; their mass defines an intrinsic >> length scale, the Compton wavelength. > > So it does, but to say the size of an object is given by the Compton > wavelength is just silly. Of course, it is silly. But I applied the Compton wavelength only to an electron, not to the sun. > Apply it to the Sun, and you can see why! > It may be that there are 'size' questions that can usefully be answered > by referring to the Compton wavelength, but it's not a generic way of > defining size. The generic way to define size is by specifying a field variable which gives the property in terms of which you want to measure size, and then looking at the region in space where the expectation of this variable has a significant support. This is how we define the size of the sun, a cloud, a soap bubble,an amoeba, an atom, a nucleus, or an electron. >>> An electron does not have welldefined component particles (virtual >>> particles don't count). >> Why don't they count? The dressed stated of an electron (with a size) >> is made up of sizeless bare electrons, in a similar way as the hydrogen >> atom (with a size) is made of an electron and a proton, except that >> the electron involves inifinitely many bare particles. > > Because they don't have any characteristic distance between them that > is a function of their interactions. Atoms in the Sun, quarks in a > proton, or bricks in a house do, because they are real particles. Nobody measures the size of the sun by the characteristic distance of the quarks it contains  they cannot even be seen. But one measures it by the radius within which the density of the matter field or the radiation field of the sun is significant. (And one gets _different_ sizes, as one can see at a total eclipse.) If you express this in terms of quantum mechanics you end up with exactly the recipe above. >>> So I think the only answer to "What size is the electron?" is "Define >>> what you mean by size." >> It is welldefined by the literature. See my theoretical physics FAQ >> at http://www.mat.univie.ac.at/~neum/physicsfaq.txt >> (Are electrons pointlike/structureless?) > > I don't believe "the size of an electron" is welldefined by the > literature. For example, your web page refers to the de Broglie > wavelength, and to the charge radius. Like the Compton wavelength, > neither of these can be considered the obvious definition of size. They are all proof of extendedness of the electron. Size is a buzzword like intensity which is formalized by refering to more specific properties and giving them more formal names. The intensity of a beam is also not uniquely defined formally, but the various measures all reflect the fact that a beam has intensity. That the radius of the sun has two different values depending on how you define it does not mean that the radius is not a meaningful measure of size. It just means that there are several measures. The same holds for an electron. > By contrast, the definition for a composite object in terms of the > characteric distances between its components is universal, and > corresponds to ordinary concepts of 'size'. Anyone can create definitions for private use only. This is just your private definition of size. In contrast to the definitions I quoted from the literature, your definition has no authoritative support. Arnold Neumaier 


#29
Apr1907, 05:00 AM

P: n/a

Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at>
>Gerry Quinn schrieb: >> In article <461E4183.2010006@univie.ac.at>, >>Arnold.Neumaier@univie.ac.at says... >>> Oh No schrieb: >>>> In the orthodox interpretation of quantum theory it only makes sense to >>>> talk of an observable quantity when a measurement is done. From that >>>> point of view the electron is sizeless. >>> From that point of view, the sun (a slightly bigger quantum object) >>> is also sizeless if nobody looks at it. Such a point of view is >>> therefore useless. >> In the first place, the Sun is a classical object; it creates lots >>of entropy, and the 'environment' is always looking at it. > >Every classical object is also a quantum object, composed of myriads >of quantum particles. How does it become classical? Precisely because it is composed of a large population of particles. > >The Environment is also always looking at a single particle. >Thus there is no difference. I can't believe you would suggest that there is no difference between the behaviour of a single particle and the behaviour of a population, which is calculated from expectation values individual particle behaviour. > > >> In the second place, the Sun differs from an electron in that it is >>composed of more than one particle, and the interactions of these >>particles define a size. The same applies to protons. Composite >>objects have a welldefined, if not always exact, size. > >And the same allies to electrons; their mass defines an intrinsic >length scale, the Compton wavelength. > You are conflating a wave function with matter. A length scale for a probability amplitude is quite a different thing from size. > >> An electron does not have welldefined component particles (virtual >>particles don't count). > >Why don't they count? Because they are not a part of an elementary particle. > >> So I think the only answer to "What size is the electron?" is "Define >>what you mean by size." > >It is welldefined by the literature. See my theoretical physics FAQ >at http://www.mat.univie.ac.at/~neum/physicsfaq.txt >(Are electrons pointlike/structureless?) > After what you said about there being no difference between a single particle and a population, I am not sure I would want to recommend anyone to look at that. > Regards  Charles Francis moderator sci.physics.foundations. substitute charles for NotI to email 


#30
Apr1907, 05:00 AM

P: n/a

Oh No schrieb:
> Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at> >> Greg McLac schrieb: >> >>> If there's only one particle, you are >>> out of luck. A wave function doesn't give several positions, there is only >>> one, that is unknown. >> As the sun, a soap bubble, or an atom, a wave function has a charge >> density and mass density, which define lengths scales. > > It does not have a density. It has an amplitude. This is a completely > different concept. And because it has an amplitude, it has a mass density, which is the expectation of a(x)^* M a(x), where M is the mass operator (usually a cnumber), and a charge density, which is the expectation of a(x)^* Q a(x), where Q is the charge operator. This is standard statistical mechanics. Arnold Neumaier 


#31
Apr2107, 05:00 AM

P: n/a

"Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote:
> And because it has an amplitude, it has a mass density, which is the > expectation of a(x)^* M a(x), where M is the mass operator (usually a > cnumber), and a charge density, which is the expectation of > a(x)^* Q a(x), where Q is the charge operator. This is standard > statistical mechanics. I'm afraid no. Even if named similar, a probability density isn't a physic density. It means that in the volume element dv, it is a probability p.dv of detect the electron at a point in the element. The probability amplitude isn't a observable like the mass density, it is associated to no operator.  Put your sig here. 


#32
Apr2207, 05:00 AM

P: n/a

In article <462639DD.6060805@univie.ac.at>,
Arnold.Neumaier@univie.ac.at says... > Gerry Quinn schrieb: > > I also mentioned that the Sun generates entropy  effectively a > > continuous blizzard of measurement events. > > No. Not the sun generates the entropy, but the approximate description > of the sun that discards all the quantum degrees of freedom. > On the fundasmental level, where the universe is a single quantum field, > there is no entropy. The latter only appears through approximations, > as you can learn from any statistical mechanics textbook. On that level of description, there is not much in the way of physics at all. But I think there is little point in further discussing this. > >> And the same allies to electrons; their mass defines an intrinsic > >> length scale, the Compton wavelength. > > > > So it does, but to say the size of an object is given by the Compton > > wavelength is just silly. > > Of course, it is silly. But I applied the Compton wavelength only > to an electron, not to the sun. The Compton wavelength has the same meaning for both. It is not 'size'. > The generic way to define size is by specifying a field variable which > gives the property in terms of which you want to measure size, and then > looking at the region in space where the expectation of this variable > has a significant support. This is how we define the size of the sun, > a cloud, a soap bubble,an amoeba, an atom, a nucleus, or an electron. That is not a good definition of size, because it includes uncertainty of position. If a fly is released in a large room, would you say it is the size of the room? > > Because they don't have any characteristic distance between them that > > is a function of their interactions. Atoms in the Sun, quarks in a > > proton, or bricks in a house do, because they are real particles. > > Nobody measures the size of the sun by the characteristic distance > of the quarks it contains  they cannot even be seen. But one measures > it by the radius within which the density of the matter field or the > radiation field of the sun is significant. (And one gets _different_ > sizes, as one can see at a total eclipse.) The quarks are in protons, which are near electrons, which emit radiation and are seen. Not that visibility defines size anyway  the quarks define it as well as the electrons. And I have never stated that there is an exact unique value, just that there is a natural way of defining size for composite objects. For elementary particles, you are trying to put forward the Compton wavelength as a substitute. But it does not represent size, but uncertainty of position, which is a different concept. > > I don't believe "the size of an electron" is welldefined by the > > literature. For example, your web page refers to the de Broglie > > wavelength, and to the charge radius. Like the Compton wavelength, > > neither of these can be considered the obvious definition of size. > > They are all proof of extendedness of the electron. A different question than whether it has a welldefined size. > > By contrast, the definition for a composite object in terms of the > > characteric distances between its components is universal, and > > corresponds to ordinary concepts of 'size'. > > Anyone can create definitions for private use only. > This is just your private definition of size. > In contrast to the definitions I quoted from the literature, > your definition has no authoritative support. It does not require authoritative support, it is a straightforward definition of the ordinary understanding of the word 'size', in physics or elsewhere. For the record, your web page has (quite sensibly) *no* definition for the size of an electron. Because for electons, there is no natural definition.  Gerry Quinn 


#33
Apr2407, 05:00 AM

P: n/a

Igor KW schrieb:
> "Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote: > >> And because it has an amplitude, it has a mass density, which is the >> expectation of a(x)^* M a(x), where M is the mass operator (usually a >> cnumber), and a charge density, which is the expectation of >> a(x)^* Q a(x), where Q is the charge operator. This is standard >> statistical mechanics. > > I'm afraid no. Even if named similar, a probability density isn't a physic > density. This has nothing to do with the name. I didn't talk about a probability density. > It means that in the volume element dv, it is a probability p.dv > of detect the electron at a point in the element. The probability amplitude > isn't a observable like the mass density, it is associated to no operator. I did't make any claim about the probability amplitude, which indeed isn't observable. But the mass and charge density are always given by the recipe I stated. You can see this by looking at the statistical mechanics formula for the mass density of a macroscopic object composed of N particles, and then reduce N one by one until you arrive at a 1particle system. If your claim were correct, you'd have to find an N where the statistical mechanics definition starts getting wrong. But there is no such N. Thus the definition of statistical mechanics remains valid for all N, including N=1. The charge density of a molecule (for which the number N of electrons ranges from 1 to many thousands), defined in this way, is indeed observable. It is one of the key quantities computed by quantum chemistry packages, as it defines the classical field which is the input for classical molecular mechanics calculations, which can be checked by experiment. Arnold Neumaier 


#34
Apr2407, 05:00 AM

P: n/a

Oh No schrieb:
> Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at> >> Gerry Quinn schrieb: >>> In article <461E4183.2010006@univie.ac.at>, >>> Arnold.Neumaier@univie.ac.at says... >>>> Oh No schrieb: >>>>> In the orthodox interpretation of quantum theory it only makes sense to >>>>> talk of an observable quantity when a measurement is done. From that >>>>> point of view the electron is sizeless. >>>> From that point of view, the sun (a slightly bigger quantum object) >>>> is also sizeless if nobody looks at it. Such a point of view is >>>> therefore useless. >>> In the first place, the Sun is a classical object; it creates lots >>> of entropy, and the 'environment' is always looking at it. >> Every classical object is also a quantum object, composed of myriads >> of quantum particles. How does it become classical? > > Precisely because it is composed of a large population of particles. How many particles must a quantum system have to become classical? >> The Environment is also always looking at a single particle. >> Thus there is no difference. > > I can't believe you would suggest that there is no difference between > the behaviour of a single particle and the behaviour of a population, > which is calculated from expectation values individual particle > behaviour. Formally, there is no difference. In each case, the laws of quantum mechanics only predict the values of formal expectations of operators over the full quantum state, and it is inconsistent to prescribe different interpretations for these expectations in the case of a single particle and a multiparticle system. Ther is no threshold when one or the other description ceases to be valid. >>> In the second place, the Sun differs from an electron in that it is >>> composed of more than one particle, and the interactions of these >>> particles define a size. The same applies to protons. Composite >>> objects have a welldefined, if not always exact, size. >> And the same allies to electrons; their mass defines an intrinsic >> length scale, the Compton wavelength. > > You are conflating a wave function with matter. A length scale for a > probability amplitude is quite a different thing from size. No. In both cases, it describes the extension of the density of the field which makes up the particle. The sun is just a bound state with a particularly large size, but intrinsically no different from a proton, a bound state of three quarks. >>> An electron does not have welldefined component particles (virtual >>> particles don't count). >> Why don't they count? > > Because they are not a part of an elementary particle. In the standard description of relativistic quantum field theory, a physical (dressed) electron is madde up of a bare electron and a variable number of virtual bare photons and electronpositron pairs, in precisely the same way as in nonrelativistic quantum mechanics, a hydrogen atom is made up of a bare proton and a bare electron. The only intrinsic difference is the variable number of particles, and the associated limiting process needed in renormalization. Arnold Neumaier 


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