Various questions

Igor Khavkine

On 2007-04-11, Greg McLac <some@thing.co.uk> wrote:
> Igor Khavkine:
>> About the "size" of an electron. Personally, I think that the standard
>> deviation of the expectation value of its charge density is as good a
>> measure of "size" as any. You may disagree.
>
> I do, because it isn't the definition of a size. According to you, a marble
> in a opaque box, then with an unknown position, has the size of the box.
> You may have a different definition of size, but it won't be the same as
> everyone.

If the box is totally opaque then I don't even know if there's a marble
inside. To put it less prosaically, both definitions of "size" I gave
are amenable to experimental measurement. It also so happens that I've
got a theory that allows me to compute the same quantity (which can then
be compared to the measured one). In your idealized situation of a
marble in a box, you're literally telling me that I can't perform any
measurements to determine what's inside the box. Then there's little
point in discussing what theoretically would be in it or how big the It
would be.

>> You may even prefer to say that the
>> concept of "size" does not apply to the electron (as you do above). This
>> is as good a position to hold as any, as long as you can articulate it.
>> Unfortunately, when someone asks "What is the size of an electron?" you
>> are stuck explaining how something may have no size (meaning that it's
>> not a point particle (meaning that it doesn't have a finite size
>> (meaning it doesn't have an infinite size either ...))). :-)
>
> What is the colour of an electron? An electron have no colour and no size,
> because there's no orbiting electrons, and because there's no characteristic
> parameter with the dimension of length in its equation. Why is that so
> difficult to understand? What's the taste of an electron? Does it taste
> like chicken?

For some reason, since childhood, I've thought that electrons are
yellow, protons are orange, and neutrons are green. But that's just me.
:-) More realistically, perceived color is determined by the response of
the cones of the human eye to electromagnetic radiation. Schematically,
the eye has three photoreceptors, each with different frequency response
curves, peacked at red, green, and blue respectively. Every color the
we perceive is a combination of signals from each of the three
photoreceptors. Once the spectrum of incoming light is known, it is not
difficult to estimate the rods' response to it. Since a moving electron
can emit light, it's spectrum can be examined (theoretically and
experimentally) and its perceived color determined. So, a moving
electron has color, and its color depends on its motion. And if the
emitted light has no appreciable overlap with the frequencies
perceptible to the human eye, then it's black. Now, the taste of an
electron is a more intriguing question... I wonder if a single electron
can have a noticible effect on our taste buds. If not, it's got to be
tasteless.

The lesson is that if a question can be reduced to something measurable,
then it usually can be answered. Even though the question might sound
silly. BTW, there is a fundamental length associated to an electron: the
Compton length = h/mc ~ 2.4*10^-12 m. Some consider it the lower bound
on the size of an electron. No, you don't have to be one of them.

>> That's an awfully complicated way to calculate size and spin. I've
>> certainly never done it this way, nor have I seen it done this way in
>> textbooks, except maybe as a heuristic explanation.
>
> Berkeley textbook about electromagnetism.

Hmm, not a QFT text. Don't see how a (possibly questionable) heuristic
calculation from that book could be a point against QFT.

>> Not sure about what
>> you mean by "bug free theory". QFT certainly has some drawbacks, both
>> mathematical and physical, but it's "bug free" enough to describe the
>> spin and charge density of an electron, has been so for over 50 years.
>> Care to share your reservations?
>
> Divergences pop up like mushrooms in a warm spring afternoon. The cupboards
> swarm with skeletons.

Divergences pop up in many places. In QFT, in particular, they are
handled with the following steps: regularization, renormalization. Both
have technical definitions and are on sound mathematical footing, as
long as one is concerned in computing things perturbatively. If you are
interested in understanding the technical details, I can explain the
basic principles and give references for further reading. As neither
cupboards nor skeletons have technical meanigs that I am aware of I
can't comment on their presence.

> The "heuristic" explanation also give a realistic
> value, a numerical coincidence isn't a proof a theory. All that only
> reflect that all the various theories try and explain the same body of data.

Theories exist to fit existing experimental data and to predict the
outcomes of future experiments. They cannot be proved, but they can be
disproved. There is no law that says that only a single theory shall fit
the data. What is the objection?

>> "unspecified quantities, that are wholeheartedly called field operator":
>> When dealing with wave functions, a state with n+1 particles is
>> created by multiplying a wave function with n particles by a
>> 1-particle wave function and (anti)symmetrizing. In field theory, a
>> state with n+1 particles is created by multiplying an n-particle state
>> by a field operator. This is consistent with the promotion of wave
>> functions to operators in second quantization.
>
> "unspecified quantities, that are wholeheartedly called creation operator".
> Surely you know the specified expression of this operator for a bosonic HO.
> Which is it for the "fermionic HO"?

The creation annihilation operators for the usual HO are a bit hard to
write out explicitly, as they are infinite dimensional. But for a
fermionic HO it's actually doable. First, algebraically:

H - Hilbert space of states, 2-dimensional
b*, b - creation annihilation operators
{b,b*} = b b* + b* b = 1 - canonical anticommutation relations
K = w b* b - Hamiltonian (sorry already used H)
Heisenberg equations of motion:
db/dt = -i [b,K] = -i w ({b,b} b* - b {b,b*}) = i w b
b(t) = b(0) exp( i w t)
b*(t) = b*(0) exp(-i w t), similarly
|0>, |1> - ground and excited states
b|0> = 0 , b*|0> = |1>
b|1> = |0>, b*|1> = 0
K|0> = 0,
K|1> = w

And now, in matrix form:

|0> = [ 1 ], |1> = [ 0 ],
[ 0 ] [ 1 ]

b(t) = [ 0 1 ] exp(i w t), b* = [ 0 0 ] exp(-i w t), K = [ 0 0 ].
[ 0 0 ] [ 1 0 ] [ 0 w ]

You can check that these matrices satisfy all the above given
properties. Is this specific enough?

>> "the whole is promoted to the pompous status of spin-statistic theorem":
>> There is a theorem called the Spin-Statistics Theorem, but I'm not
>> sure how it can be pompous. It is applicable to relativistically
>> invariant field theories in 4 dimensions. Once you know that
>> quantizing (fermions) bosons requires the introduction of
>> (anti)commutation relations, it says that you cannot quantize an
>> integer spin field as a fermion, nor a half-integer spin field as a
>> boson. However, once you relax the hypotheses, the theorem no longer
>> applies. For example, non-relativistic theories allow fermions to have
>> integral spin. Also, when you go down some dimensions, bosons and
>> fermions can have any spin. For instance, spinless fermions are used
>> often in toy models of condensed matter theory, where models with only
>> 1 or 2 spatial dimensions are common.
>
> It says that you can't quantize a fermion with commutators. Much ado for
> nothing. We already empirically know that half-integer spin particles obey
> the Fermi-Dirac statistics. What does this theorem learn us?

Let me repeat in a play by play. Suppose we have three theoretical
hypotheses: (A) elementary particles are described by 4-dimensional
relativistically invariant field theory, (B) elementary particles are
described by 4-dimensional non-relativistic field theory, (C)
elementary particles are described by field theory with 2 or 3
dimensions.

Ignore for the moment any prodiction of either hypothesis beside the
connection between spin and statistics. In answer to the question "Can
there exist bosons of half-integral spin or fermions of integral spin?"
each hypothesis answers: (A) No, (B) Yes, (C) Yes.

Let's look at the empirical data: So far, neither half-integral spin
bosons nor integral spin fermions have been observed.

How does each hypothesis fare in the face of empirical data?
(A) Consistent, (B) Consistent, (C) Consistent.

Hmm, how about some more empirical data: "So far" means over a long
period of time and over a wide energy range.

The theoretical picture is now somewhat different.
(A) Consistent, (B) Consistent, but highly unlikely, (C) Consistent, but
highly unlikely.

And finally, if ever we do in deed discover an elementary particle that
is either a half-integral spin boson or an integral spin fermion, then
we get: (A) Inconsistent, (B) Consistent, (C) Consistent.

In other words, the connection between spin and statistics is a firm
prediction of some theoretical hypotheses. The empirical connection
between spin and statistics allows us to falsify some of these
hypotheses and to classify others as likely or unlikely. That's science.

> Toy models are fun, but space-time is actually 3+1 dimensional.

In deed. However, if you think that all 2+1 dimensional models are toys,
the Nobel prizes handed for the quantum Hall effect say otherwise.

Finally, let me repeat and rephrase a statement I made earlier: the
anticommutation relations for fermionic field operators are a direct
consequence, through second quantization, of indistinguishability of
fermionic particles and their statistics. You said that it was vague.
Now, what part(s) of it do you think vague? If I know, I may be able to
correct that impression.

Igor

Oh No

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

Gerry Quinn

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 well-defined, if not always exact, size.

An electron does not have well-defined 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

Gerry Quinn

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 well-defined, if not always exact, size.

An electron does not have well-defined 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

Gerry Quinn

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 well-defined, if not always exact, size.

An electron does not have well-defined 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

Arnold Neumaier

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 well-defined, 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 well-defined 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 well-defined by the literature. See my theoretical physics FAQ
at http://www.mat.univie.ac.at/~neum/physics-faq.txt
(Are electrons pointlike/structureless?)


Arnold Neumaier

Greg McLac

Arnold Neumaier:
> And chemists measure the size of atoms in terms of the charge density of
> their electron cloud, which is state-dependent.
>
> 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 state-dependent 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

Arnold Neumaier

Greg McLac schrieb:
> Arnold Neumaier:
>> And chemists measure the size of atoms in terms of the charge density of
>> their electron cloud, which is state-dependent.
>>
>> 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 state-dependent 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 well-defined position and hence not a
well-defined distance???


> An atom is made of at least two particles, so the same
> definition applies, even if fuzzy.

And this size is obviously state-dependent, since it depends on where
these particles may be. The only state-independent 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
state-independent.


> 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
X-rays), 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

Gerry Quinn

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 well-defined, 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 well-defined 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 well-defined by the literature. See my theoretical physics FAQ
> at http://www.mat.univie.ac.at/~neum/physics-faq.txt
> (Are electrons pointlike/structureless?)

I don't believe "the size of an electron" is well-defined 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 well-defined size.

- Gerry Quinn

Oh No

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 state-dependent, since it depends on where
>these particles may be. The only state-independent 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
>state-independent.

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

Arnold Neumaier

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 well-defined, 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 well-defined 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 well-defined by the literature. See my theoretical physics FAQ
>> at http://www.mat.univie.ac.at/~neum/physics-faq.txt
>> (Are electrons pointlike/structureless?)
>
> I don't believe "the size of an electron" is well-defined 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

Oh No

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 well-defined, 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 well-defined 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 well-defined by the literature. See my theoretical physics FAQ
>at http://www.mat.univie.ac.at/~neum/physics-faq.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

Arnold Neumaier

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
c-number), 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

Igor KW

"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
> c-number), 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.

Gerry Quinn

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 well-defined 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 well-defined 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

Arnold Neumaier

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
>> c-number), 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 1-particle 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

Arnold Neumaier

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 well-defined, 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 well-defined 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 electron-positron 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