What is classical - what quantum?
Peter
In order to find out, where classical and where quantum statistical
mechanics apply, we need to find out:
What is classical - what quantum?
Let's start with
What is a classical particle (body) - what a quantum particle?
I'm quite sure, that the following definition is useful.
The essence of the classical bodies is their impenetrability.
(Euler)
>From this, the other 3 most general properties extension, movability
and inertia follow, and also that they move along trajectories. Space
and time are presupposed as in the 'Principia'. For treating gravity,
one has to add the general property of gravitating mass (Newton).
Now, I don't know how to formulate a definition of comparable
conciseness for quantum particles: Please help!
Thank you very much in advance!
Peter
Oh No
>Dear all,
>
>In order to find out, where classical and where quantum statistical
>mechanics apply, we need to find out:
>
> What is classical - what quantum?
>
>Let's start with
>
> What is a classical particle (body) - what a quantum particle?
>
>I'm quite sure, that the following definition is useful.
>
> The essence of the classical bodies is their impenetrability.
>(Euler)
We are talking of statistical mechanics, and hence of gases. These are
not impenetrable.
>
>>From this, the other 3 most general properties extension, movability
>and inertia follow, and also that they move along trajectories. Space
>and time are presupposed as in the 'Principia'. For treating gravity,
>one has to add the general property of gravitating mass (Newton).
>
>Now, I don't know how to formulate a definition of comparable
>conciseness for quantum particles: Please help!
You asked this question a little while ago. My answer was
Certainly we must define CM and QM before answering the question, but
this will not do. The first is tautology and takes us nowhere, the
second is not true.
I would propose, as an initial definition which may later be generalised
(and will need to be e.g. for gases), that
classical mechanics is the mechanics of bodies whose position can be
continuously known up to the limit of experimental accuracy.
quantum mechanics is the mechanics of particles whose position cannot be
known between observations even in principle
I have not found a similarly succinct definition to incorporate gases,
but I would accept the notion that a gas is classical, even though the
particles of a gas are not. Hence I would seek some sort of definition
based on the gas laws.
Regards
--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)
Bob_for_short
It is a very hard question: nobody knows the answer because there is a
dualism.
I personally think that the quantum is what is quantified, the
classical is what is classified.
Bob.
======================================= MODERATOR'S COMMENT:
lol
Bob_for_short
and a long talk.
I said: "Everybody understands Classical Mechanics". R. Feynman sipped
his coffee and replied:
"Nobody understands Quantum Mechanics". We shook hands and went each
in his direction.
Bob.
tnlo...@aol.com
Peter;
In my opinion, there is not a definable "quantum" particle. All
subatomic particles must have the measurable characteristics such as
mass, spin, charge and magnetic moment.
I remember a conference lecture by a group who did some successful
precision mesurements on the electron.
They mentioned they had presented their test plans at their University
and an irate physicist got up and walked out claiming the uncertainty
principle would make the measurement impossible. Of course he was
shown to wrong by their later results.
Once during my other life, I was a Supervisor of a Component Test
Lab.
We screened electrical component parts for use in high reliability
equipment.
The screening tests required that a sample size was greater than 5 so
that the testing would be "statistically significant".
The failure rate of the sample had a "bathtub" curve. The failure
rate was initially high, and then bottom out making the remaining
sample screened for use in high reliability equipment.
Excess failure rates disqualified the manufacturer as a source.
So my view of "statistical" is the probability that a sample size of
at least 5 is being considered.
Quantum mechanics uses statistics with out specifiying the (at least)
five (5) variables making things statistically significant.
Quantum mechanics is so counter intuitive that it is safe to say "No
one understands quantum mechanics."
I suspect the word quantum mechanics wins arguements by making the
debate opponents retreat in utter confusion.
Regards; Tom
Amazon.com 096315463X
Oh No
>at least 5 is being considered.
I would suggest caution. It does of course depend on the precise test
under consideration, but in undergrad lectures on statistics at
Cambridge it was shown that, as a rule of thumb, for a typical test, a
sample size of at least about 13-14 is necessary for a statistically
significant result. More recently I have been doing tests on spiral arm
structure. Astrophysicists have published results using samples of as
few as 18 star forming regions in the galaxy, and have claimed that
these results indicate that the galaxy has four spiral arms. But because
of the number of free parameters you would need hundreds of data points
for any sort of meaningful result. I cannot help but think that the
statistical training of scientists for statistical science is somewhat
lacking, for otherwise prominent scientists would never have tried to
publish such results, and reviewers would never have accepted them.
>Quantum mechanics uses statistics with out specifiying the (at least)
>five (5) variables making things statistically significant.
>
Quantum mechanics uses probability theory, on which statistics is based.
It does not use statistics as such.
The meaning of probability theory has itself been the subject of much
historical debate. If we find it hard to understand the interpretation
of probability theory, then it will be harder still to understand the
meaning of quantum mechanics. The more traditional frequency
interpretation of probability theory is now felt not to hold, and most
theorists accept a Bayesian interpretation. There is still debate
between objective and subjective Bayesianism. Subjective Bayesianism is
perfectly valid, and can be used when only an intuitive notion of
likelihood is available, but the "logic of science" requires objective
Bayesianism, as described by Jaynes.
>Quantum mechanics is so counter intuitive that it is safe to say "No
>one understands quantum mechanics."
This was true when Feynman originally said it, but it is not safe to
continue to say it, or to dismiss out of hand work which has been done
more recently.
http://www.teleconnection.info/rqg/FoundationsOfQuantumTheory
Peter
> >Dear all,
>
> >In order to find out, where classical and where quantum statistical
> >mechanics apply, we need to find out:
>
> > What is classical - what quantum?
>
> >Let's start with
>
> > What is a classical particle (body) - what a quantum particle?
>
> >I'm quite sure, that the following definition is useful.
>
> > The essence of the classical bodies is their impenetrability.
> >(Euler)
> We are talking of statistical mechanics, and hence of gases. These are
> not impenetrable.
Sorry, I'm speaking here about classical bodies. Later, I will
consider (classical) gases of such impenetrable bodies (the gas itself
is not impenetrable, of course).
> >From this, the other 3 most general properties extension, movability
> >and inertia follow, and also that they move along trajectories. Space
> >and time are presupposed as in the 'Principia'. For treating gravity,
> >one has to add the general property of gravitating mass (Newton).
>
> >Now, I don't know how to formulate a definition of comparable
> >conciseness for quantum particles: Please help!
> You asked this question a little while ago. My answer was
>
> Certainly we must define CM and QM before answering the question, but
> this will not do. The first is tautology and takes us nowhere, the
> second is not true.
I don't understand this remark, I'm afraid. To define CM as the
mechanics of impenetrable bodies is not a tautology.
My question is: Can one define quantum particles independent of QM
(being the mechanics of such particles)?
> I would propose, as an initial definition which may later be generalised
> (and will need to be e.g. for gases), that
>
> classical mechanics is the mechanics of bodies whose position can be
> continuously known up to the limit of experimental accuracy.
Thus, classical bodies those objects which are located at positions, r
(t), where r(t) is - within the limit of experimental accuracy - a
continuous function of the continuous parameter t (time) (trajectory).
This provides a good discrimination against quantum particles, but
lacks extension, movability and inertia.
> quantum mechanics is the mechanics of particles whose position cannot be
> known between observations even in principle
This gives a good discrimination against classical particles, but it
suffers from the general disadvantage of negative definitions, that
often the posive properties does not follow uniquely.
> I have not found a similarly succinct definition to incorporate gases,
> but I would accept the notion that a gas is classical, even though the
> particles of a gas are not. Hence I would seek some sort of definition
> based on the gas laws.
This is dangerous, because the laws are approximations and
'historically not stable'
Thank you,
Peter
Peter
> > Dear all,
>
> > In order to find out, where classical and where quantum statistical
> > mechanics apply, we need to find out:
>
> > What is classical - what quantum?
>
> > Let's start with
>
> > What is a classical particle (body) - what a quantum particle?
>
> > I'm quite sure, that the following definition is useful.
>
> > The essence of the classical bodies is their impenetrability.
> > (Euler)
>
> > From this, the other 3 most general properties extension, movability
> > and inertia follow, and also that they move along trajectories. Space
> > and time are presupposed as in the 'Principia'. For treating gravity,
> > one has to add the general property of gravitating mass (Newton).
>
> > Now, I don't know how to formulate a definition of comparable
> > conciseness for quantum particles: Please help!
>
> > Thank you very much in advance!
> > Peter
> Peter;
>
> In my opinion, there is not a definable "quantum" particle. All
> subatomic particles must have the measurable characteristics such as
> mass, spin, charge and magnetic moment.
The latter is correct, but it gives no reason why there should not be
a definition as straight as that for the classical body.
...
> So my view of "statistical" is the probability that a sample size of
> at least 5 is being considered.
I remember '6' for making rough statements about mean value and
standard deviation ("rough", because it's insufficient for applying
Gaussian fault analysis). The statistics in QM has nothing to do with
that; it speaks about probabilities, ie, the outcome of infinitely
many measurements (sample size = oo)
> Quantum mechanics uses statistics with out specifiying the (at least)
> five (5) variables making things statistically significant.
sample size = oo
> Quantum mechanics is so counter intuitive that it is safe to say "No
> one understands quantum mechanics."
I anticipate Charles' answer which will enlighten that this depends on
what means "understand".
> I suspect the word quantum mechanics wins arguements by making the
> debate opponents retreat in utter confusion.
I would not apply this to Schrödinger's work :-)
Thank you,
Peter
Oh No
>On 22 Apr., 00:09, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
>> >Dear all,
>>
>> >In order to find out, where classical and where quantum statistical
>> >mechanics apply, we need to find out:
>>
>> > What is classical - what quantum?
>>
>> >Let's start with
>>
>> > What is a classical particle (body) - what a quantum particle?
>>
>> >I'm quite sure, that the following definition is useful.
>>
>> > The essence of the classical bodies is their impenetrability.
>> >(Euler)
>
>
>> We are talking of statistical mechanics, and hence of gases. These are
>> not impenetrable.
>
>Sorry, I'm speaking here about classical bodies. Later, I will
>consider (classical) gases of such impenetrable bodies (the gas itself
>is not impenetrable, of course).
Yes. The definitions I give below suffer from the same failing (not
applying to gases). I agree that we need to address bodies first.
>> >From this, the other 3 most general properties extension, movability
>> >and inertia follow, and also that they move along trajectories. Space
>> >and time are presupposed as in the 'Principia'. For treating gravity,
>> >one has to add the general property of gravitating mass (Newton).
>>
>> >Now, I don't know how to formulate a definition of comparable
>> >conciseness for quantum particles: Please help!
>
>
>> You asked this question a little while ago. My answer was
>>
>> Certainly we must define CM and QM before answering the question, but
>> this will not do. The first is tautology and takes us nowhere, the
>> second is not true.
>
>I don't understand this remark, I'm afraid. To define CM as the
>mechanics of impenetrable bodies is not a tautology.
Sorry. Careless pasting on my part. This referred to a previous post.
Best ignored here.
>
>My question is: Can one define quantum particles independent of QM
>(being the mechanics of such particles)?
>
>
>> I would propose, as an initial definition which may later be generalised
>> (and will need to be e.g. for gases), that
>>
>> classical mechanics is the mechanics of bodies whose position can be
>> continuously known up to the limit of experimental accuracy.
>
>Thus, classical bodies those objects which are located at positions, r
>(t), where r(t) is - within the limit of experimental accuracy - a
>continuous function of the continuous parameter t (time) (trajectory).
>This provides a good discrimination against quantum particles, but
>lacks extension, movability and inertia.
These properties may reasonably added, but as a defining condition I
don't think it is far out. "Position" probably needs to be generalised,
to incorporate extension - not simply position of the centre of gravity.
>
>> quantum mechanics is the mechanics of particles whose position cannot be
>> known between observations even in principle
>
>This gives a good discrimination against classical particles, but it
>suffers from the general disadvantage of negative definitions, that
>often the posive properties does not follow uniquely.
Yes, but I don't have a better one, and I haven't found a way to see
that this particular negative definition fails.
>> I have not found a similarly succinct definition to incorporate gases,
>> but I would accept the notion that a gas is classical, even though the
>> particles of a gas are not. Hence I would seek some sort of definition
>> based on the gas laws.
>
>This is dangerous, because the laws are approximations and
>'historically not stable'
>
Good point. Any positive suggestions?
Peter
> >> >Dear all,
>
> >> >In order to find out, where classical and where quantum statistical
> >> >mechanics apply, we need to find out:
>
> >> > What is classical - what quantum?
>
> >> >Let's start with
>
> >> > What is a classical particle (body) - what a quantum particle?
>
> >> >I'm quite sure, that the following definition is useful.
>
> >> > The essence of the classical bodies is their impenetrability.
> >> >(Euler)
> >> We are talking of statistical mechanics, and hence of gases. These are
> >> not impenetrable.
> >Sorry, I'm speaking here about classical bodies. Later, I will
> >consider (classical) gases of such impenetrable bodies (the gas itself
> >is not impenetrable, of course).
> Yes. The definitions I give below suffer from the same failing (not
> applying to gases). I agree that we need to address bodies first.
very good :-)
> >> >From this, the other 3 most general properties extension, movability
> >> >and inertia follow, and also that they move along trajectories. Space
> >> >and time are presupposed as in the 'Principia'. For treating gravity,
> >> >one has to add the general property of gravitating mass (Newton).
> >> >
> >> >Now, I don't know how to formulate a definition of comparable
> >> >conciseness for quantum particles: Please help!
...
> >My question is: Can one define quantum particles independent of QM
> >(being the mechanics of such particles)?
> >> I would propose, as an initial definition which may later be generalised
> >> (and will need to be e.g. for gases), that
> >>
> >> classical mechanics is the mechanics of bodies whose position can be
> >> continuously known up to the limit of experimental accuracy.
> >Thus, classical bodies those objects which are located at positions, r
> >(t), where r(t) is - within the limit of experimental accuracy - a
> >continuous function of the continuous parameter t (time) (trajectory).
> >This provides a good discrimination against quantum particles, but
> >lacks extension, movability and inertia.
> These properties may reasonably added, but as a defining condition I
> don't think it is far out. "Position" probably needs to be generalised,
> to incorporate extension - not simply position of the centre of gravity.
Correct - in order to avoid the ad-hoc addition of new definitions/
postulates lateron, I would like to have one comprehensive one from
the very beginning. For this, I have proposed to choose
impenetrability (De gravitatione...) and gravitating mass (Principia)
as the constituting properties of classical bodies.
> >> quantum mechanics is the mechanics of particles whose position cannot be
> >> known between observations even in principle
> >This gives a good discrimination against classical particles, but it
> >suffers from the general disadvantage of negative definitions, that
> >often the posive properties does not follow uniquely.
> Yes, but I don't have a better one, and I haven't found a way to see
> that this particular negative definition fails.
The same with me - for this, I have opened this thread
> >> I have not found a similarly succinct definition to incorporate gases,
> >> but I would accept the notion that a gas is classical, even though the
> >> particles of a gas are not. Hence I would seek some sort of definition
> >> based on the gas laws.
> >This is dangerous, because the laws are approximations and
> >'historically not stable'
> Good point. Any positive suggestions?
Gibbs works with ensembles of particles, this circumvents those
problems.
Thank you,
Peter
Oh No
>On 22 Apr., 13:58, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
> ...
>> >My question is: Can one define quantum particles independent of QM
>> >(being the mechanics of such particles)?
>
>
>> >> I would propose, as an initial definition which may later be generalised
>> >> (and will need to be e.g. for gases), that
>> >>
>> >> classical mechanics is the mechanics of bodies whose position can be
>> >> continuously known up to the limit of experimental accuracy.
>
>
>> >Thus, classical bodies those objects which are located at positions, r
>> >(t), where r(t) is - within the limit of experimental accuracy - a
>> >continuous function of the continuous parameter t (time) (trajectory).
>> >This provides a good discrimination against quantum particles, but
>> >lacks extension, movability and inertia.
>
>
>> These properties may reasonably added, but as a defining condition I
>> don't think it is far out. "Position" probably needs to be generalised,
>> to incorporate extension - not simply position of the centre of gravity.
>
>Correct - in order to avoid the ad-hoc addition of new definitions/
>postulates lateron, I would like to have one comprehensive one from
>the very beginning. For this, I have proposed to choose
>impenetrability (De gravitatione...) and gravitating mass (Principia)
>as the constituting properties of classical bodies.
I don't see the special significance of impenetrability, or of
gravitating mass to a definition. Clearly I don't deny the fact that
mass gravitates, but I think that even in the absence of quantum gravity
we may reasonably think that the mass of quantum particles also
gravitates, and we can perfectly well form classical laws in the absence
of a gravitational field.
>> >> quantum mechanics is the mechanics of particles whose position cannot be
>> >> known between observations even in principle
>
>> >This gives a good discrimination against classical particles, but it
>> >suffers from the general disadvantage of negative definitions, that
>> >often the posive properties does not follow uniquely.
>
>> Yes, but I don't have a better one, and I haven't found a way to see
>> that this particular negative definition fails.
>
>The same with me - for this, I have opened this thread
>
>
>> >> I have not found a similarly succinct definition to incorporate gases,
>> >> but I would accept the notion that a gas is classical, even though the
>> >> particles of a gas are not. Hence I would seek some sort of definition
>> >> based on the gas laws.
>
>> >This is dangerous, because the laws are approximations and
>> >'historically not stable'
>
>> Good point. Any positive suggestions?
>
>Gibbs works with ensembles of particles, this circumvents those
>problems.
But this raises the thorny issue of whether those particles can be
regarded as classical or not - something on which I believe we disagree.
This may still be the way forward, if it is agreed that the particles of
a classical gas can be quantum.
Peter
I try to build the theory of classical bodies (quantum particles) from
the properties of them. Impenetrability is all what one needs for the
mechanics of impacts. The failure of Euler to derive the force of
gravity from that interaction strongly supports Newton's view
(spacetime is given, thus, GTR is not yet considered).
Can you derive Newton's gravity force law without assigning to the
bodies gravitating mass?
...
> >> >> I have not found a similarly succinct definition to incorporate gases,
> >> >> but I would accept the notion that a gas is classical, even though the
> >> >> particles of a gas are not. Hence I would seek some sort of definition
> >> >> based on the gas laws.
>
> >> >This is dangerous, because the laws are approximations and
> >> >'historically not stable'
>
> >> Good point. Any positive suggestions?
>
> >Gibbs works with ensembles of particles, this circumvents those
> >problems.
>
> But this raises the thorny issue of whether those particles can be
> regarded as classical or not - something on which I believe we disagree.
It seems so, and I don't understand, why.
Speeding ahead:
An ensamble (gas) of impenetrable bodies builds a classical ensemble;
there is no de Broglie wavelength indicating qualitative changes when
crossed by the mean particle distance, no Bose-Einstein condensation
or Wigner cristallization, etc.
i) Gibbs 1902, Ch. XV: The thermodynamical properties of a (classical)
gas are not changed, when 2 equal particles with equal velocities are
interchanged. Do you agree with this?
I cannot see that this observation on a classical gas has anything to
do with quantum - do you?
ii) Gibbs, loc. cit.: Consequently, the distribution function, D, of a
(classical) gas is not changed, when 2 equal particles with equal
velocities are interchanged (IMHO, his notion of generic phase is not
the clearest one, where D=exp{Phase}). Do you agree with this?
I cannot see that this statement has anything to do with quantum - do
you?
iii) Hence, any method for calculating the distribution function and
the thermodynamical potentials, in particular, the entropy, is correct
only, if it yields the observations (i) and (ii). Do you agree with
this?
I cannot see that this statement has anything to do with quantum - do
you?
(iv) Hence, the counting of microstates in Boltzmann's counting method
for calculating the entropy is correct only, if it yields the
observations (i) and (ii). Do you agree with this?
I cannot see anything 'quantum' in counting classical (micro-)states
for sets of classical bodies - do you?
(v) Microstate 1:
Box 1: Body 1 - Box 2: Body 2
Microstate 2:
Box 1: Body 2 - Box 2: Body 1
Why it should be 'classical' to count both microstates
*thermodynamically* different and 'quantum' to count them
*thermodynamically* equal? What is the physics ('one can mark the
bodies' is no physics) behind these notations?
I guess a misunderstanding of the role of the single-body states;
perhaps, the conclusion was: motion in phase space => Laplacian notion
of state. In contrast, consider a gas with Maxwell distribution and
account for the fact, the Eulerian (stationary) state of this gas,
which comprises the set of all body velocities, is permutation
invariant... -
As a matter of fact, counting both microstates yields wrong results
for the classical entropy of a classical gas (Gibbs' paradox). Hence,
this counting is not 'classical', but plain wrong.
Counting only one of them yields correct results for the classical
entropy of a classical gas (no Gibbs' paradox). Hence, this counting
is not 'quantum', but correct.
Of course, the always distinguishability of impenetrable bodies
(through their non-overlapping trajectories) seduces to assign the
missing factor 1/N! to it. But this is neither methodologically
satisfying, nor correct. For the correct counting yields the Planck
distribution (Bose-Einstein without chemical potential - I don't know
yet, how exactly the latter enters, do you?), *not* Boltzmann with 1/
N!...
> This may still be the way forward, if it is agreed that the particles of
> a classical gas can be quantum.
You don't need to, see above :-)
Thank you,
Peter
Oh No
We need conservation of momentum, plus a notion of elasticity (energy
loss) for impacts, and impacts are not all of classical mechanics. I do
not see the relevance of impenetrability anyway. What about friction.
What if a projectile is fired into a rubber ball and becomes embedded in
it. Can we not deal with that problem in classical mechanics? I
contradicts impenatribility.
> The failure of Euler to derive the force of
>gravity from that interaction strongly supports Newton's view
>(spacetime is given, thus, GTR is not yet considered).
>
>Can you derive Newton's gravity force law without assigning to the
>bodies gravitating mass?
This does not seem relevant to the question. gravity does not (as far as
we know) differentiate between quantum and classical.
>> >> >> I have not found a similarly succinct definition to incorporate gases,
>> >> >> but I would accept the notion that a gas is classical, even though the
>> >> >> particles of a gas are not. Hence I would seek some sort of definition
>> >> >> based on the gas laws.
>>
>> >> >This is dangerous, because the laws are approximations and
>> >> >'historically not stable'
>>
>> >> Good point. Any positive suggestions?
>>
>> >Gibbs works with ensembles of particles, this circumvents those
>> >problems.
>>
>> But this raises the thorny issue of whether those particles can be
>> regarded as classical or not - something on which I believe we disagree.
>
>It seems so, and I don't understand, why.
The definition I gave above is why. I do not think it possible in
principle to assign position to each and every particle in a gas.
>
>Speeding ahead:
>An ensamble (gas) of impenetrable bodies builds a classical ensemble;
>there is no de Broglie wavelength indicating qualitative changes when
>crossed by the mean particle distance, no Bose-Einstein condensation
>or Wigner cristallization, etc.
>
>i) Gibbs 1902, Ch. XV: The thermodynamical properties of a (classical)
>gas are not changed, when 2 equal particles with equal velocities are
>interchanged. Do you agree with this?
I am no expert, but as I understand it, yes.
>I cannot see that this observation on a classical gas has anything to
>do with quantum - do you?
>
It follows naturally if we are not able to assign position to the
individual particles of the gas.
>ii) Gibbs, loc. cit.: Consequently, the distribution function, D, of a
>(classical) gas is not changed, when 2 equal particles with equal
>velocities are interchanged (IMHO, his notion of generic phase is not
>the clearest one, where D=exp{Phase}). Do you agree with this?
>
>I cannot see that this statement has anything to do with quantum - do
>you?
yes, for the reasons you give below.
The definition I have given of particles of gas as classical bodies
would cause these to be different. Clearly this gives the wrong answer.
>Counting only one of them yields correct results for the classical
>entropy of a classical gas (no Gibbs' paradox). Hence, this counting
>is not 'quantum', but correct.
The definition I have given of particles of gas as quantum bodies
results in this correct counting.
>
>Of course, the always distinguishability of impenetrable bodies
>(through their non-overlapping trajectories) seduces to assign the
>missing factor 1/N! to it.
Exactly.
> But this is neither methodologically
>satisfying, nor correct. For the correct counting yields the Planck
>distribution (Bose-Einstein without chemical potential - I don't know
>yet, how exactly the latter enters, do you?), *not* Boltzmann with 1/
>N!...
>
>
>> This may still be the way forward, if it is agreed that the particles of
>> a classical gas can be quantum.
>
>You don't need to, see above :-)
I do by the definitions I have given. Otherwise one would count
incorrectly, as you have shown.
Peter
still
yes - does it follow from your proposed definition of CM?
>From the impenetrability, you can derive (!) Newton's eq. of motion,
and from this the Lagrange formalism in the usual manner (where there
are steps I'm not happy with), which provides you with the
conservation laws
> plus a notion of elasticity (energy loss) for impacts,
eventually yes - does it follow from your proposed definition of CM?
energy loss at impacts means heat being outside CM - I'm still at the
stage of classical point mechanics, because the mechanics of rotating
bodies needs additional postulates (after Euler, the symmetry of the
tensor of inertia cannot be derived from the principles of point
mechanics); let's go step by step and not putting all things in the
pan from the beginning ;-)
> and impacts are not all of classical mechanics.
indeed - but let's proceed step by step:
- the impenetrability is sufficient for the mechanics of elastic
impacts; there is a complete axiomatics which should be helpful as
model theory and thus guide;
- it is not sufficient for gravitation, let's add the least necessary
amount, etc.
please notice, that the mechanics of impacts exhibits none interaction
constant, - isn't this an argument in favour of that the can serve as
protophysics?
> I do not see the relevance of impenetrability anyway.
It should help you to think about, why
- it was important for Newton and Euler,
- it played a role during the invention and development of quantum
theory (see Mehra & Rechenberg)
- it still is invoked in the discussions about the realtionship
between classical and quantum statistics...
How do you guarantee the principal distinguishability of classical
bodies? (You have evoked it before!)
> What about friction.
Within CM, one can treat is only phenomenologically, thus, this is
outside the scope of this thread.
> What if a projectile is fired into a rubber ball and becomes embedded in it.
On his way, the projectile has shifted away any rubber matter: perfect
non-penetration
> Can we not deal with that problem in classical mechanics?
only phenomenologically; while the impenetrability provides a
sufficient reason for the forces during impact, no CM reason can be
given for heat production
> It contradicts impenatribility.
No, it does not, see above - impenetrability is to be understood not
just geometrically, but also dynamically
"Forces occur is just that amount which is necessary to prevent the
mutual penetration of two bodies" (Euler, 'Anleitung zur Naturlehre',
'Sur l'origin des forces', 'Lettres à une Princesse Allémagne'),
since
"It is impossible that two bodies occupy the same space" (ibid.)
The latter principle has been stressed already by Newton (De
gravitatione...) - since it doesn't play any role for the planetary
motion, it is not particularly mentioned in the 'Principia'
> > The failure of Euler to derive the force of
> >gravity from that interaction strongly supports Newton's view
> >(spacetime is given, thus, GTR is not yet considered).
>
> >Can you derive Newton's gravity force law without assigning to the
> >bodies gravitating mass?
> This does not seem relevant to the question. gravity does not (as far as
> we know) differentiate between quantum and classical.
For this differentiation, it is not relevant, but it is for the
foundation of CM
>
>
>
> >> >> >> I have not found a similarly succinct definition to incorporate gases,
> >> >> >> but I would accept the notion that a gas is classical, even though the
> >> >> >> particles of a gas are not. Hence I would seek some sort of definition
> >> >> >> based on the gas laws.
>
> >> >> >This is dangerous, because the laws are approximations and
> >> >> >'historically not stable'
>
> >> >> Good point. Any positive suggestions?
>
> >> >Gibbs works with ensembles of particles, this circumvents those
> >> >problems.
>
> >> But this raises the thorny issue of whether those particles can be
> >> regarded as classical or not - something on which I believe we disagree.
>
> >It seems so, and I don't understand, why.
>
> The definition
of what?
> I gave above is why. I do not think it possible in
> principle to assign position to each and every particle in a gas.
Within CM, for a gas of classical bodies, it is (I'm not disputing
Laplace's daemon)
>
>
>
> >Speeding ahead:
> >An ensamble (gas) of impenetrable bodies builds a classical ensemble;
> >there is no de Broglie wavelength indicating qualitative changes when
> >crossed by the mean particle distance, no Bose-Einstein condensation
> >or Wigner cristallization, etc.
>
> >i) Gibbs 1902, Ch. XV: The thermodynamic properties of a (classical)
> >gas are not changed, when 2 equal particles with equal velocities are
> >interchanged. Do you agree with this?
>
> I am no expert, but as I understand it, yes.
Thank you :-)
>
> >I cannot see that this observation on a classical gas has anything to
> >do with quantum - do you?
>
> It follows naturally if we are not able to assign position to the
> individual particles of the gas.
This looks formally correct, but
- what the ability of mankind has to do with the laws of nature?
- how your reply is related to my question?
>
>
> >ii) Gibbs, loc. cit.: Consequently, the distribution function, D, of a
> >(classical) gas is not changed, when 2 equal particles with equal
> >velocities are interchanged (IMHO, his notion of generic phase is not
> >the clearest one, where D=exp{Phase}). Do you agree with this?
>
Do you agree with this?
>
> >I cannot see that this statement has anything to do with quantum - do
> >you?
>
> yes, for the reasons you give below.
>
there are many - which ones exactly?
>
>
> >iii) Hence, any method for calculating the distribution function and
> >the thermodynamical potentials, in particular, the entropy, is correct
> >only, if it yields the observations (i) and (ii). Do you agree with
> >this?
>
> >I cannot see that this statement has anything to do with quantum - do
> >you?
Does your non-reply means, that you also don't see anything?
>
>
> >(iv) Hence, the counting of microstates in Boltzmann's counting method
> >for calculating the entropy is correct only, if it yields the
> >observations (i) and (ii). Do you agree with this?
Dis I overlook your reply?
>
> >I cannot see anything 'quantum' in counting classical (micro-)states
> >for sets of classical bodies - do you?
>
> >(v) Microstate 1:
>
> > Box 1: Body 1 - Box 2: Body 2
>
> >Microstate 2:
>
> > Box 1: Body 2 - Box 2: Body 1
>
> >Why it should be 'classical' to count both microstates
> >*thermodynamically* different and 'quantum' to count them
> >*thermodynamically* equal? What is the physics ('one can mark the
> >bodies' is no physics) behind these notations?
>
> >I guess a misunderstanding of the role of the single-body states;
> >perhaps, the conclusion was: motion in phase space => Laplacian notion
> >of state. In contrast, consider a gas with Maxwell distribution and
> >account for the fact, the Eulerian (stationary) state of this gas,
> >which comprises the set of all body velocities, is permutation
> >invariant... -
>
> >As a matter of fact, counting both microstates yields wrong results
> >for the classical entropy of a classical gas (Gibbs' paradox). Hence,
> >this counting is not 'classical', but plain wrong.
>
>
>
> The definition I have given of particles of gas as classical bodies
> would cause these to be different.
Why, wher is which cause?
Please explain it in detail for the sake of your own understanding!
> Clearly this gives the wrong answer.
For this, I have asked you to provide and thus rethink the reasoning
(I'm not your enemy :-)
> >Counting only one of them yields correct results for the classical
> >entropy of a classical gas (no Gibbs' paradox). Hence, this counting
> >is not 'quantum', but correct.
>
> The definition I have given of particles of gas as quantum bodies
> results in this correct counting.
Yes - but what about a gas of classical bodies?
Are there no classical bodies?
Is classical statistical mechanics not self-consistent?
>
>
>
> >Of course, the always distinguishability of impenetrable bodies
> >(through their non-overlapping trajectories) seduces to assign the
> >missing factor 1/N! to it.
>
> Exactly.
>
> > But this is neither methodologically
> >satisfying, nor correct. For the correct counting yields the Planck
> >distribution (Bose-Einstein without chemical potential - I don't know
> >yet, how exactly the latter enters, do you?), *not* Boltzmann with 1/
> >N!...
your reply?
missing reply indicates 'seduction fine' ;-)
>
> >> This may still be the way forward, if it is agreed that the particles of
> >> a classical gas can be quantum.
>
> >You don't need to, see above :-)
>
> I do by the definitions I have given. Otherwise one would count
> incorrectly, as you have shown.
Your definitions are inappropriate :-)
Thank you,
Peter
Oh No
No. (So far I have only tried to define classical bodies, btw.) For
classical mechanics I would have to take conservation of momentum as a
fundamental principle, because I don't like the Lagrangian formulation.
For quantum theory it can be proven, and from there it can be carried
into the classical domain.
>
>>From the impenetrability, you can derive (!) Newton's eq. of motion,
>and from this the Lagrange formalism in the usual manner (where there
>are steps I'm not happy with), which provides you with the
>conservation laws
>
>> plus a notion of elasticity (energy loss) for impacts,
>
>eventually yes - does it follow from your proposed definition of CM?
Depends exactly what we choose as fundamental law, but we need non-
conservative forces at a fairly early stage, I would think. It is
possible they are better expressed as energy loss than as force - Just
as I prefer conservation of momentum as a fundamental principle to
Newton's laws.
>
>energy loss at impacts means heat being outside CM
Yes. So we need this as a fundamental of CM.
>- I'm still at the
>stage of classical point mechanics, because the mechanics of rotating
>bodies needs additional postulates (after Euler, the symmetry of the
>tensor of inertia cannot be derived from the principles of point
>mechanics); let's go step by step and not putting all things in the
>pan from the beginning ;-)
>
>> and impacts are not all of classical mechanics.
>
>indeed - but let's proceed step by step:
>- the impenetrability is sufficient for the mechanics of elastic
>impacts; there is a complete axiomatics which should be helpful as
>model theory and thus guide;
>- it is not sufficient for gravitation, let's add the least necessary
>amount, etc.
I don't see impenetrability as sufficient for elastic impacts, because
there are also non-elastic impacts. Something more would be needed.
>
>please notice, that the mechanics of impacts exhibits none interaction
>constant, - isn't this an argument in favour of that the can serve as
>protophysics?
>
>> I do not see the relevance of impenetrability anyway.
>
>It should help you to think about, why
>- it was important for Newton and Euler,
>- it played a role during the invention and development of quantum
>theory (see Mehra & Rechenberg)
>- it still is invoked in the discussions about the realtionship
>between classical and quantum statistics...
>
>How do you guarantee the principal distinguishability of classical
>bodies? (You have evoked it before!)
I have answered this question twice already.
>
>> What about friction.
>
>Within CM, one can treat is only phenomenologically, thus, this is
>outside the scope of this thread.
No. Friction forces are part of classical mechanics, and cannot be
ignored.
>
>> What if a projectile is fired into a rubber ball and becomes embedded in it.
>
>On his way, the projectile has shifted away any rubber matter: perfect
>non-penetration
What if the projectile is a liquid.
>
>> Can we not deal with that problem in classical mechanics?
>
>only phenomenologically; while the impenetrability provides a
>sufficient reason for the forces during impact, no CM reason can be
>given for heat production
I would disagree. Seems to me that all classical laws are
phenomenological as you say, though I would not disparage that and I
would call them empirical.
>
>> It contradicts impenatribility.
>
>No, it does not, see above - impenetrability is to be understood not
>just geometrically, but also dynamically
>
>"Forces occur is just that amount which is necessary to prevent the
>mutual penetration of two bodies" (Euler, 'Anleitung zur Naturlehre',
>'Sur l'origin des forces', 'Lettres à une Princesse Allémagne'),
If that were true, all collisions would be perfectly inelastic.
>
>since
>
>"It is impossible that two bodies occupy the same space" (ibid.)
>
>The latter principle has been stressed already by Newton (De
>gravitatione...) - since it doesn't play any role for the planetary
>motion, it is not particularly mentioned in the 'Principia'
>
sounds like Euler got it wrong, to me.
of classical bodies and of quantum particles.
>
>> I gave above is why. I do not think it possible in
>> principle to assign position to each and every particle in a gas.
>
>Within CM, for a gas of classical bodies, it is (I'm not disputing
>Laplace's daemon)
Are we talking about the behaviour of matter, or about some sort of
idealised metaphysics.
>>
>>
>>
>> >Speeding ahead:
>> >An ensamble (gas) of impenetrable bodies builds a classical ensemble;
>> >there is no de Broglie wavelength indicating qualitative changes when
>> >crossed by the mean particle distance, no Bose-Einstein condensation
>> >or Wigner cristallization, etc.
>>
>> >i) Gibbs 1902, Ch. XV: The thermodynamic properties of a (classical)
>> >gas are not changed, when 2 equal particles with equal velocities are
>> >interchanged. Do you agree with this?
>>
>> I am no expert, but as I understand it, yes.
>
>Thank you :-)
>>
>> >I cannot see that this observation on a classical gas has anything to
>> >do with quantum - do you?
>>
>> It follows naturally if we are not able to assign position to the
>> individual particles of the gas.
>
>This looks formally correct, but
>- what the ability of mankind has to do with the laws of nature?
>- how your reply is related to my question?
It is the laws of nature which prevent us from assigning position to
each individual particle. Thus your "classical gas" does not appear to
be real.
>> >ii) Gibbs, loc. cit.: Consequently, the distribution function, D, of a
>> >(classical) gas is not changed, when 2 equal particles with equal
>> >velocities are interchanged (IMHO, his notion of generic phase is not
>> >the clearest one, where D=exp{Phase}). Do you agree with this?
>>
>Do you agree with this?
I cannot agree with "consequently", as I have not seen his argument.
>>
>> >I cannot see that this statement has anything to do with quantum - do
>> >you?
>>
>> yes, for the reasons you give below.
>>
>there are many - which ones exactly?
As I recall, they all boil down to the fact of not being able to assign
position to particles individually
>>
>> >iii) Hence, any method for calculating the distribution function and
>> >the thermodynamical potentials, in particular, the entropy, is correct
>> >only, if it yields the observations (i) and (ii). Do you agree with
>> >this?
>>
>> >I cannot see that this statement has anything to do with quantum - do
>> >you?
>
>Does your non-reply means, that you also don't see anything?
No. it means that I do not see the point of repeating the same reply
many times.
>>
>>
>> >(iv) Hence, the counting of microstates in Boltzmann's counting method
>> >for calculating the entropy is correct only, if it yields the
>> >observations (i) and (ii). Do you agree with this?
>
>Dis I overlook your reply?
ditto
>>
>> >I cannot see anything 'quantum' in counting classical (micro-)states
>> >for sets of classical bodies - do you?
>>
>> >(v) Microstate 1:
>>
>> > Box 1: Body 1 - Box 2: Body 2
>>
>> >Microstate 2:
>>
>> > Box 1: Body 2 - Box 2: Body 1
>>
>> >Why it should be 'classical' to count both microstates
>> >*thermodynamically* different and 'quantum' to count them
>> >*thermodynamically* equal? What is the physics ('one can mark the
>> >bodies' is no physics) behind these notations?
>>
>> >I guess a misunderstanding of the role of the single-body states;
>> >perhaps, the conclusion was: motion in phase space => Laplacian notion
>> >of state. In contrast, consider a gas with Maxwell distribution and
>> >account for the fact, the Eulerian (stationary) state of this gas,
>> >which comprises the set of all body velocities, is permutation
>> >invariant... -
>>
>> >As a matter of fact, counting both microstates yields wrong results
>> >for the classical entropy of a classical gas (Gibbs' paradox). Hence,
>> >this counting is not 'classical', but plain wrong.
>>
>>
>>
>> The definition I have given of particles of gas as classical bodies
>> would cause these to be different.
>
>Why, wher is which cause?
>Please explain it in detail for the sake of your own understanding!
Don't be so bloody conceited and rude. You are the one having trouble
with a simple concept.
>
>> Clearly this gives the wrong answer.
>
>For this, I have asked you to provide and thus rethink the reasoning
>(I'm not your enemy :-)
>
>> >Counting only one of them yields correct results for the classical
>> >entropy of a classical gas (no Gibbs' paradox). Hence, this counting
>> >is not 'quantum', but correct.
>>
>> The definition I have given of particles of gas as quantum bodies
>> results in this correct counting.
>
>Yes - but what about a gas of classical bodies?
Is there such a thing?
>
>Are there no classical bodies?
Clearly
>
>Is classical statistical mechanics not self-consistent?
The only statistical mechanics I ever studied was heavily dependent on
quantum theory, since classical mechanics is not sufficient to describe
the underlying processes.
>>
>> >Of course, the always distinguishability of impenetrable bodies
>> >(through their non-overlapping trajectories) seduces to assign the
>> >missing factor 1/N! to it.
>>
>> Exactly.
>>
>> > But this is neither methodologically
>> >satisfying, nor correct. For the correct counting yields the Planck
>> >distribution (Bose-Einstein without chemical potential - I don't know
>> >yet, how exactly the latter enters, do you?), *not* Boltzmann with 1/
>> >N!...
>
>your reply?
This has already been answered. Your repetition is childish, and I will
not rise to it.
>missing reply indicates 'seduction fine' ;-)
Is it a Freudian slip that you talk of seduction rather than deduction?
>>
>> >> This may still be the way forward, if it is agreed that the particles of
>> >> a classical gas can be quantum.
>>
>> >You don't need to, see above :-)
>>
>> I do by the definitions I have given. Otherwise one would count
>> incorrectly, as you have shown.
>
>Your definitions are inappropriate :-)
your behaviour is inappropriate. My definitions have given a complete
and simple account of every point you have raised, and you have
responded by failing to think and with ill manners.
tnlo...@aol.com
> Thus spake "tnlock...@aol.com" <tnlock...@aol.com>
>
> >On Apr 21, 12:36_pm, Peter <end...@dekasges.de> wrote:
> >> Dear all,
>
> >So my view of "statistical" is the probability that a sample size of
> >at least 5 is being considered.
>
> I would suggest caution. It does of course depend on the precise test
> under consideration, but in undergrad lectures on statistics at
> Cambridge it was shown that, as a rule of thumb, for a typical test, a
> sample size of at least about 13-14 is necessary for a statistically
> significant result.
Yes, we would not disqualify a manufacturer on sample sizes less than
24.
>More recently I have been doing tests on spiral arm
> structure. Astrophysicists have published results using samples of as
> few as 18 star forming regions in the galaxy, and have claimed that
> these results indicate that the galaxy has four spiral arms. But because
> of the number of free parameters you would need hundreds of data points
> for any sort of meaningful result. I cannot help but think that the
> statistical training of scientists for statistical science is somewhat
> lacking, for otherwise prominent scientists would never have tried to
> publish such results, and reviewers would never have accepted them.
Yes, it is good to take that conservative approach.
We had the use of Reliability Engineers to help keep us reasonable.
> >Quantum mechanics uses statistics with out specifiying the (at least)
> >five (5) variables making things statistically significant.
> Quantum mechanics uses probability theory, on which statistics is based.
> It does not use statistics as such.
>
> The meaning of probability theory has itself been the subject of much
> historical debate. If we find it hard to understand the interpretation
> of probability theory, then it will be harder still to understand the
> meaning of quantum mechanics. The more traditional frequency
> interpretation of probability theory is now felt not to hold, and most
> theorists accept a Bayesian interpretation. There is still debate
> between objective and subjective Bayesianism. Subjective Bayesianism is
> perfectly valid, and can be used when only an intuitive notion of
> likelihood is available, but the "logic of science" requires objective
> Bayesianism, as described by Jaynes.
Yes, but Engineers like to have a probability of one so everything is
a sure thing. ;-)
> >Quantum mechanics is so counter intuitive that it is safe to say "No
> >one understands quantum mechanics."
>
> This was true when Feynman originally said it, but it is not safe to
> continue to say it, or to dismiss out of hand work which has been done
> more recently.http://www.teleconnection.info/rqg/FoundationsOfQuantumTheory
I just took a quick look your WEB page, and find it is a complete
overview of quantum mechanics, Charles, thanks for your good work.
As Wheeler said, "If you would learn, teach"
Regards; Tom
Amazon.com 096315463X
Peter
Momentum conservation should be a consequence of the properties of the
bodies - I forsee, that else you will permanently be compelled to add
ad-hoc new postulates.
> For
> classical mechanics I would have to take conservation of momentum as a
> fundamental principle, because I don't like the Lagrangian formulation.
> For quantum theory it can be proven,
Perhaps by means of too many assumptions
> and from there it can be carried
> into the classical domain.
>
>
>
In contrast, within an Eulerian approach to CM, you don't need any
additional assumption for getting it, as I wrote before:
> >From the impenetrability, you can derive (!) Newton's eq. of motion,
> >and from this the Lagrange formalism in the usual manner (where there
> >are steps I'm not happy with), which provides you with the
> >conservation laws
>
> >> plus a notion of elasticity (energy loss) for impacts,
>
> >eventually yes - does it follow from your proposed definition of CM?
>
> Depends exactly what we choose as fundamental law, but we need non-
> conservative forces at a fairly early stage, I would think. It is
> possible they are better expressed as energy loss than as force -
Where do you get 'energy' from?
> Just
> as I prefer conservation of momentum as a fundamental principle to
> Newton's laws.
Newton's laws are an unappropriate starting point for constructing CM,
because Law 2 prevents the generalization to other branches.
>
>
>
> >energy loss at impacts means heat being outside CM
>
> Yes. So we need this as a fundamental of CM.
one cannot take something as fundamental what is outside :-o
Let me recall what I wrote before:
> >- I'm still at the
> >stage of classical point mechanics, because the mechanics of rotating
> >bodies needs additional postulates (after Euler, the symmetry of the
> >tensor of inertia cannot be derived from the principles of point
> >mechanics); let's go step by step and not putting all things in the
> >pan from the beginning ;-)
> >> and impacts are not all of classical mechanics.
>
> >indeed - but let's proceed step by step:
> >- the impenetrability is sufficient for the mechanics of elastic
> >impacts; there is a complete axiomatics which should be helpful as
> >model theory and thus guide;
> >- it is not sufficient for gravitation, let's add the least necessary
> >amount, etc.
>
> I don't see impenetrability as sufficient for elastic impacts, because
> there are also non-elastic impacts. Something more would be needed.
Having thought about that, I'm not sure, if inelastic impacts cannot
be included, though heat production can be treated only
phenomenologically as an addendum (friction forces etc.)
Impenetrability gives you
d[f(v)v] = 1/m F dt
f(v) describes the dependence of the change of v by F on the current
value of v (Newton and Euler assumed silently f==1) - In principle, F
can be any function of v
>
>
> >please notice, that the mechanics of impacts exhibits none interaction
> >constant, - isn't this an argument in favour of that the can serve as
> >protophysics?
> >> I do not see the relevance of impenetrability anyway.
>
> >It should help you to think about, why
> >- it was important for Newton and Euler,
> >- it played a role during the invention and development of quantum
> >theory (see Mehra & Rechenberg)
> >- it still is invoked in the discussions about the realtionship
> >between classical and quantum statistics...
>
> >How do you guarantee the principal distinguishability of classical
> >bodies? (You have evoked it before!)
>
> I have answered this question twice already.
I remember that you have indicated the non-overlapping of the
trajectories of all parts of the bodies, this would be sufficient
>
>
> >> What about friction.
>
> >Within CM, one can treat is only phenomenologically, thus, this is
> >outside the scope of this thread.
>
> No. Friction forces are part of classical mechanics, and cannot be
> ignored.
I'm not ignoring it (see above), but it's not fundamental for CM
>
>
>
> >> What if a projectile is fired into a rubber ball and becomes embedded in it.
>
> >On his way, the projectile has shifted away any rubber matter: perfect
> >non-penetration
>
> What if the projectile is a liquid.
no difference; the pores are not part of the rubber
>
>
>
> >> Can we not deal with that problem in classical mechanics?
>
> >only phenomenologically; while the impenetrability provides a
> >sufficient reason for the forces during impact, no CM reason can be
> >given for heat production
>
> I would disagree. Seems to me that all classical laws are
> phenomenological as you say, though I would not disparage that and I
> would call them empirical.
No, many laws can be derived from the impenetrability and, hence, are
not "phenomenological", or "empirical". Newton's force law can be
derived from his definition of the bodies in the 'Principia' (letting
aside the weaknesses in 'The Definitions'), but I would be wondering,
if this would be possible for F_friction=-k.v.
>
>
>
> >> It contradicts impenatribility.
>
> >No, it does not, see above - impenetrability is to be understood not
> >just geometrically, but also dynamically
>
> >"Forces occur is just that amount which is necessary to prevent the
> >mutual penetration of two bodies" (Euler, 'Anleitung zur Naturlehre',
> >'Sur l'origin des forces', 'Lettres à une Princesse Allémagne'),
>
> If that were true, all collisions would be perfectly inelastic.
I cannot follow, how did you get that?
>
> >since
> >"It is impossible that two bodies occupy the same space" (ibid.)
>
> >The latter principle has been stressed already by Newton (De
> >gravitatione...) - since it doesn't play any role for the planetary
> >motion, it is not particularly mentioned in the 'Principia'
>
> sounds like Euler got it wrong, to me.
Euler got the gravitation wrong, but his axiomatics is superior to
Newton's one in that it can be generalized, while Newton's one cannot
>
>
>
> >> > The failure of Euler to derive the force of
> >> >gravity from that interaction strongly supports Newton's view
> >> >(spacetime is given, thus, GTR is not yet considered).
>
> >> >Can you derive Newton's gravity force law without assigning to the
> >> >bodies gravitating mass?
>
> >> This does not seem relevant to the question. gravity does not (as far as
> >> we know) differentiate between quantum and classical.
you wish to have friction from the very beginning, but not gravity :-o
...
>
> >> >> >> >> I have not found a similarly succinct definition to
> >> >> >> >>incorporate gases,
> >> >> >> >> but I would accept the notion that a gas is classical, even
> >> >> >> >>though the
> >> >> >> >> particles of a gas are not. Hence I would seek some sort of
> >> >> >> >>definition
> >> >> >> >> based on the gas laws.
>
> >> >> >> >This is dangerous, because the laws are approximations and
> >> >> >> >'historically not stable'
>
> >> >> >> Good point. Any positive suggestions?
>
> >> >> >Gibbs works with ensembles of particles, this circumvents those
> >> >> >problems.
>
> >> >> But this raises the thorny issue of whether those particles can be
> >> >> regarded as classical or not - something on which I believe we disagree.
>
> >> >It seems so, and I don't understand, why.
>
> >> The definition
>
> >of what?
>
> of classical bodies and of quantum particles.
>
>
>
> >> I gave above is why. I do not think it possible in
> >> principle to assign position to each and every particle in a gas.
>
> >Within CM, for a gas of classical bodies, it is (I'm not disputing
> >Laplace's daemon)
>
> Are we talking about the behaviour of matter, or about some sort of
> idealised metaphysics.
we speak about how to build descriptions of the behaviour of matter
assuming your definition of classical bodies/particles, you can assign
a trajectory to each one and, thus, a position at any time, correct?
what is the difference to having put some millions of them into a box?
btw, it does not need any quantum theory to treat the air pressure in
a car tyre
>
>
>
> >> >Speeding ahead:
> >> >An ensamble (gas) of impenetrable bodies builds a classical ensemble;
> >> >there is no de Broglie wavelength indicating qualitative changes when
> >> >crossed by the mean particle distance, no Bose-Einstein condensation
> >> >or Wigner cristallization, etc.
>
> >> >i) Gibbs 1902, Ch. XV: The thermodynamic properties of a (classical)
> >> >gas are not changed, when 2 equal particles with equal velocities are
> >> >interchanged. Do you agree with this?
>
> >> I am no expert, but as I understand it, yes.
>
> >Thank you :-)
>
> >> >I cannot see that this observation on a classical gas has anything to
> >> >do with quantum - do you?
>
> >> It follows naturally if we are not able to assign position to the
> >> individual particles of the gas.
what is "naturally" and what has it to do with "to assign a position"?
> >This looks formally correct, but
> >- what the ability of mankind has to do with the laws of nature?
> >- how your reply is related to my question?
> It is the laws of nature which prevent us from assigning position to
> each individual particle.
Which "laws of nature" exactly?
see also my example of few millions particles (small classical bodies)
in a box
> Thus your "classical gas" does not appear to be real.
It is as good an approximation as many other physical models - Gibbs
assumes trajectories for all particles and gets correct results =>
your (still unfounded) claim, one cannot assign positions in a
classical gas, is not tenable
> >> >ii) Gibbs, loc. cit.: Consequently, the distribution function, D, of a
> >> >(classical) gas is not changed, when 2 equal particles with equal
> >> >velocities are interchanged (IMHO, his notion of generic phase is not
> >> >the clearest one, where D=exp{Phase}). Do you agree with this?
>
> >Do you agree with this?
>
> I cannot agree with "consequently", as I have not seen his argument.
His argument is in (i) above
>
>
>
> >> >I cannot see that this statement has anything to do with quantum - do
> >> >you?
>
> >> yes, for the reasons you give below.
>
> >there are many - which ones exactly?
>
> As I recall, they all boil down to the fact of not being able to assign
> position to particles individually
as noted above, Gibbs did it and got correct results
>
note: next point (ii) continues form (ii) above
>
> >> >iii) Hence, any method for calculating the distribution function and
> >> >the thermodynamical potentials, in particular, the entropy, is correct
> >> >only, if it yields the observations (i) and (ii). Do you agree with
> >> >this?
>
> >> >I cannot see that this statement has anything to do with quantum - do
> >> >you?
>
Best wishes,
Peter
Oh No
This is nonsense. Momentum conservation is well known to be a
consequence of the homogeneity of space. If you introduce ad hoc
assumptions which are known to be wrong I foresee that you will
permanently be compelled to ignore physics and to fantasise about your
own metaphysics.
>
>> For
>> classical mechanics I would have to take conservation of momentum as a
>> fundamental principle, because I don't like the Lagrangian formulation.
>> For quantum theory it can be proven,
>
>Perhaps by means of too many assumptions
You are the one suggesting an unnecessary, and false, assumption.
>> and from there it can be carried
>> into the classical domain.
>>
>>
>>
>In contrast, within an Eulerian approach to CM, you don't need any
>additional assumption for getting it, as I wrote before:
>> >From the impenetrability, you can derive (!) Newton's eq. of motion,
>> >and from this the Lagrange formalism in the usual manner (where there
>> >are steps I'm not happy with), which provides you with the
>> >conservation laws
>>
>
>
>> >> plus a notion of elasticity (energy loss) for impacts,
>>
>> >eventually yes - does it follow from your proposed definition of CM?
>>
>> Depends exactly what we choose as fundamental law, but we need non-
>> conservative forces at a fairly early stage, I would think. It is
>> possible they are better expressed as energy loss than as force -
>
>Where do you get 'energy' from?
In the first instance, from Newton's laws, but in a modern treatment,
from the time component of momentum.
>
>> Just
>> as I prefer conservation of momentum as a fundamental principle to
>> Newton's laws.
>
>Newton's laws are an unappropriate starting point for constructing CM,
>because Law 2 prevents the generalization to other branches.
This is nonsense. Newton's laws are the starting point for CM. To that
we may add Maxwell's equations, The Navier-Stokes equation, gas laws
>> >energy loss at impacts means heat being outside CM
>>
>> Yes. So we need this as a fundamental of CM.
>
>one cannot take something as fundamental what is outside :-o
Again you are talking nonsense. By your definition there is no classical
mechanics, because it can all be bases on things which are outside CM.
>
>Let me recall what I wrote before:
>
>> >- I'm still at the
>> >stage of classical point mechanics, because the mechanics of rotating
>> >bodies needs additional postulates (after Euler, the symmetry of the
>> >tensor of inertia cannot be derived from the principles of point
>> >mechanics); let's go step by step and not putting all things in the
>> >pan from the beginning ;-)
>
>
>
>> >> and impacts are not all of classical mechanics.
>>
>> >indeed - but let's proceed step by step:
>> >- the impenetrability is sufficient for the mechanics of elastic
>> >impacts; there is a complete axiomatics which should be helpful as
>> >model theory and thus guide;
>
>> >- it is not sufficient for gravitation, let's add the least necessary
>> >amount, etc.
>>
>> I don't see impenetrability as sufficient for elastic impacts, because
>> there are also non-elastic impacts. Something more would be needed.
>
>Having thought about that, I'm not sure, if inelastic impacts cannot
>be included, though heat production can be treated only
>phenomenologically as an addendum (friction forces etc.)
As is so for all of classical mechanics, though as I have said, your use
of "phenomentogical" is inappropriate.
.
>
>Impenetrability gives you
> d[f(v)v] = 1/m F dt
>
>f(v) describes the dependence of the change of v by F on the current
>value of v (Newton and Euler assumed silently f==1) - In principle, F
>can be any function of v
I don't see where this comes from, but if it is necessary to assume in
addition that f==1 then clearly impenetribility on its own gives you
nothing much of value.
>> I would disagree. Seems to me that all classical laws are
>> phenomenological as you say, though I would not disparage that and I
>> would call them empirical.
>
>No, many laws can be derived from the impenetrability and, hence, are
>not "phenomenological", or "empirical".
Is not impenetribility empirical. Anyway, you have just shown that
nothing much of interest can be derived from impenetribility.
>>
>> >> It contradicts impenatribility.
>>
>> >No, it does not, see above - impenetrability is to be understood not
>> >just geometrically, but also dynamically
>>
>> >"Forces occur is just that amount which is necessary to prevent the
>> >mutual penetration of two bodies" (Euler, 'Anleitung zur Naturlehre',
>> >'Sur l'origin des forces', 'Lettres à une Princesse Allémagne'),
>>
>> If that were true, all collisions would be perfectly inelastic.
>
>I cannot follow, how did you get that?
It is a trivial consequence of the quote.
>> >since
>> >"It is impossible that two bodies occupy the same space" (ibid.)
>>
>> >The latter principle has been stressed already by Newton (De
>> >gravitatione...) - since it doesn't play any role for the planetary
>> >motion, it is not particularly mentioned in the 'Principia'
>>
>> sounds like Euler got it wrong, to me.
>
>Euler got the gravitation wrong, but his axiomatics is superior to
>Newton's one in that it can be generalized, while Newton's one cannot
But the quote above shows he was talking nonsense. Anyway Euler was
largely responsible for the Euler-Lagrange equation, and all that
nonsense which has so misguided modern investigations in physics.
>> >> > The failure of Euler to derive the force of
>> >> >gravity from that interaction strongly supports Newton's view
>> >> >(spacetime is given, thus, GTR is not yet considered).
>>
>> >> >Can you derive Newton's gravity force law without assigning to the
>> >> >bodies gravitating mass?
>>
>> >> This does not seem relevant to the question. gravity does not (as far as
>> >> we know) differentiate between quantum and classical.
>
>you wish to have friction from the very beginning, but not gravity :-o
I thought the question was to differentiate quantum from classical.
Having done so, we can write down whatever body of laws we choose to
describe behaviour.
>> >> I gave above is why. I do not think it possible in
>> >> principle to assign position to each and every particle in a gas.
>>
>> >Within CM, for a gas of classical bodies, it is (I'm not disputing
>> >Laplace's daemon)
>>
>> Are we talking about the behaviour of matter, or about some sort of
>> idealised metaphysics.
>
>we speak about how to build descriptions of the behaviour of matter
>
>assuming your definition of classical bodies/particles, you can assign
>a trajectory to each one and, thus, a position at any time, correct?
>
>what is the difference to having put some millions of them into a box?
I do not know how to do that. I only know how to put many more orders of
magnitude than millions of gas particles into a box.
>>
>> >> >Speeding ahead:
>> >> >An ensamble (gas) of impenetrable bodies builds a classical ensemble;
>> >> >there is no de Broglie wavelength indicating qualitative changes when
>> >> >crossed by the mean particle distance, no Bose-Einstein condensation
>> >> >or Wigner cristallization, etc.
>>
>> >> >i) Gibbs 1902, Ch. XV: The thermodynamic properties of a (classical)
>> >> >gas are not changed, when 2 equal particles with equal velocities are
>> >> >interchanged. Do you agree with this?
>>
>> >> I am no expert, but as I understand it, yes.
>>
>> >Thank you :-)
>>
>> >> >I cannot see that this observation on a classical gas has anything to
>> >> >do with quantum - do you?
>>
>> >> It follows naturally if we are not able to assign position to the
>> >> individual particles of the gas.
>
>what is "naturally" and what has it to do with "to assign a position"?
"naturally" refers to simple logic. Not being able to assign a position
to individual gas particles means that we cannot count different states
when two identical particles are interchanged. In fact this is far too
simple to require explanation.
>
>> >This looks formally correct, but
>> >- what the ability of mankind has to do with the laws of nature?
>> >- how your reply is related to my question?
>
>> It is the laws of nature which prevent us from assigning position to
>> each individual particle.
>
>Which "laws of nature" exactly?
The behaviour of matter. Please stop playing games.
>
>see also my example of few millions particles (small classical bodies)
>in a box
I saw it, and have already pointed out that it is nonsense. Please do
not ignore everything which is said. You are pretending complications
where there are none.
>
>> Thus your "classical gas" does not appear to be real.
>
>It is as good an approximation as many other physical models - Gibbs
>assumes trajectories for all particles and gets correct results =>
>your (still unfounded) claim, one cannot assign positions in a
>classical gas, is not tenable
As I see it, you have shown that if one can assign positions, then Gibbs
has the wrong answer, and that this is not the behaviour of matter.
>> >> >ii) Gibbs, loc. cit.: Consequently, the distribution function, D, of a
>> >> >(classical) gas is not changed, when 2 equal particles with equal
>> >> >velocities are interchanged (IMHO, his notion of generic phase is not
>> >> >the clearest one, where D=exp{Phase}). Do you agree with this?
>>
>> >Do you agree with this?
>>
>> I cannot agree with "consequently", as I have not seen his argument.
>
>His argument is in (i) above
However (i) is not true for what you call a classical gas, but it is
true if the particles are treated quantum mechanically.
>> >> >I cannot see that this statement has anything to do with quantum - do
>> >> >you?
>>
>> >> yes, for the reasons you give below.
>>
>> >there are many - which ones exactly?
>>
>> As I recall, they all boil down to the fact of not being able to assign
>> position to particles individually
>
>as noted above, Gibbs did it and got correct results
No he did not, for he assumed (i).
Juan R.
(...)
>> >since
>> >"It is impossible that two bodies occupy the same space" (ibid.)
>>
>> >The latter principle has been stressed already by Newton (De
>> >gravitatione...) - since it doesn't play any role for the planetary
>> >motion, it is not particularly mentioned in the 'Principia'
>>
>> sounds like Euler got it wrong, to me.
>
>>Euler got the gravitation wrong, but his axiomatics is superior to
>>Newton's one in that it can be generalized, while Newton's one cannot
>
> But the quote above shows he was talking nonsense. Anyway Euler was
> largely responsible for the Euler-Lagrange equation, and all that
> nonsense which has so misguided modern investigations in physics.
I have sniped many paragraphs writen in inadequate language and some few
mistakes. But this part of the message could confound some readers.
Euler may have done mistakes (just as everyone does). However, the Euler-
Lagrange equations are not nonsense. They are an useful theoretical tool
for solving problems, and this explain their central role in "modern
investigations in physics".
Of course, another issue is if those equations are or not over-
evaluated by some authors. Personally, I am aware that not any dynamical
problem can be solved by them. But, I remark again, the Euler-Lagrange
equations are not nonsense
http://en.wikipedia.org/wiki/Euler-Lagrange_equation
http://mathworld.wolfram.com/Euler-LagrangeDifferentialEquation.html
--
http://www.canonicalscience.org/
Usenet Guidelines:
http://www.canonicalscience.org/en/miscellaneouszone/guidelines.html
Peter
> >> >> We need conservation of momentum,
>
> >> >yes - does it follow from your proposed definition of CM?
>
> >> No. (So far I have only tried to define classical bodies, btw.)
>
> >Momentum conservation should be a consequence of the properties of the
> >bodies - I forsee, that else you will permanently be compelled to add
> >ad-hoc new postulates.
>
> This is nonsense. Momentum conservation is well known to be a
> consequence of the homogeneity of space.
Below you write that you have to postulate it - such confusion will
never lead to serious science, I'm afraid to have to say
As well known, the bodies are supposed to be in spacetime which itself
is homogeneous and isotropic
> If you introduce ad hoc
> assumptions which are known to be wrong I foresee that you will
> permanently be compelled to ignore physics and to fantasise about your
> own metaphysics.
I regret that you are unable or unwilling to understand even a small
piece of Euler's approach to CM
>
>
>
> >> For
> >> classical mechanics I would have to take conservation of momentum as a
> >> fundamental principle, because I don't like the Lagrangian formulation.
> >> For quantum theory it can be proven,
>
> >Perhaps by means of too many assumptions
>
> You are the one suggesting an unnecessary, and false, assumption.
My "Perhaps by means of too many assumptions" was in your style of
adding one unfounded claim after the other, in order to demonstrate
you that this leads to nothing => you should return to bring forward
arguments, as (partially) at the beginning of this thread (if not,
discussion is meaningless)
>
>
> >> and from there it can be carried
> >> into the classical domain.
This I'm not denying - but as you switched to gases some postings
before, I have extended the topic from classical (and quantum) bodies
to CM
> >In contrast, within an Eulerian approach to CM, you don't need any
> >additional assumption for getting it, as I wrote before:
> >> >From the impenetrability, you can derive (!) Newton's eq. of motion,
> >> >and from this the Lagrange formalism in the usual manner (where there
> >> >are steps I'm not happy with), which provides you with the
> >> >conservation laws
> >> >> plus a notion of elasticity (energy loss) for impacts,
>
> >> >eventually yes - does it follow from your proposed definition of CM?
>
> >> Depends exactly what we choose as fundamental law, but we need non-
> >> conservative forces at a fairly early stage, I would think. It is
> >> possible they are better expressed as energy loss than as force -
>
> >Where do you get 'energy' from?
>
> In the first instance, from Newton's laws, but in a modern treatment,
> from the time component of momentum.
Ok, if there is a fine axiomatics for that, I'm happy to accept it,
and if it's better than our Eulerian approach, I'm happy to replace
the latter with that modern one. (I'm not insisting on the long
Eulerian way, but I have not yet found a more stringent one.)
> >> Just
> >> as I prefer conservation of momentum as a fundamental principle to
> >> Newton's laws.
>
> >Newton's laws are an unappropriate starting point for constructing CM,
> >because Law 2 prevents the generalization to other branches.
>
> This is nonsense.
Bohr, Heisenberg, Schrödinger are nonsense - sorry, that's not the
level to discuss at
> Newton's laws are the starting point for CM.
This is nonsense, because there are several starting points possible.
(BTW, in case you will eventually read it, you will observe that
Newton's 'Principia' itself doesn't start with the Laws.)
> To that
> we may add Maxwell's equations,
As I have foreseen: you add and add and add...
> The Navier-Stokes equation, gas laws
Can probably largely derived (analogously to the Maxwell equations)
>
>
> >> >energy loss at impacts means heat being outside CM
>
> >> Yes. So we need this as a fundamental of CM.
>
> >one cannot take something as fundamental what is outside :-o
>
> Again you are talking nonsense. By your definition there is no classical
> mechanics, because it can all be bases on things which are outside CM.
It is favourable to command some basic knowledge on elementary logics
before commenting on elementary conclusions and trying to formulate
own conclusions ;-)
...
> >> I don't see impenetrability as sufficient for elastic impacts, because
> >> there are also non-elastic impacts. Something more would be needed.
>
> >Having thought about that, I'm not sure, if inelastic impacts cannot
> >be included, though heat production can be treated only
> >phenomenologically as an addendum (friction forces etc.)
>
> As is so for all of classical mechanics, though as I have said, your use
> of "phenomentogical" is inappropriate.
There is, perhaps, a difference between the English and German
understanding of this word
>
>
> >Impenetrability gives you
> > d[f(v)v] = 1/m F dt
>
> >f(v) describes the dependence of the change of v by F on the current
> >value of v (Newton and Euler assumed silently f==1) - In principle, F
> >can be any function of v
>
> I don't see where this comes from,
I have derived it earlier in this group)
> but if it is necessary to assume in
> addition that f==1 then clearly impenetribility on its own gives you
> nothing much of value.
As I wrote: It is favourable to command some basic knowledge on
elementary logics before commenting on elementary conclusions and
trying to formulate own conclusions: I have written, that Newton and
Euler have silently assumed f==1, ie, v-independent, I have not
written that this assumption is necessary.
If F depends on v as state variable, as in the magnetic Maxwell-
Lorentz force, q v x B, f(v) becomes the Lorentz factor.
> >> I would disagree. Seems to me that all classical laws are
> >> phenomenological as you say, though I would not disparage that and I
> >> would call them empirical.
>
> >No, many laws can be derived from the impenetrability and, hence, are
> >not "phenomenological", or "empirical".
>
> Is not impenetribility empirical.
Yes, in the same sense and extent as Newton's Laws
> Anyway, you have just shown that
> nothing much of interest can be derived from impenetribility.
No, you have shown that you are unable or unwilling to learn what can
(and what cannot) derived from it, I'm afraid to have to said.
...
> >Euler got the gravitation wrong, but his axiomatics is superior to
> >Newton's one in that it can be generalized, while Newton's one cannot
>
> But the quote above shows he was talking nonsense.
Again, this is not the level to discuss at
> Anyway Euler was
> largely responsible for the Euler-Lagrange equation, and all that
> nonsense which has so misguided modern investigations in physics.
This is not only many levels below serious, but so wrong against
undisputed knowledge, that it even violates our charter, I'm afraid to
have to say
...
> >you wish to have friction from the very beginning, but not gravity :-o
>
> I thought the question was to differentiate quantum from classical.
Yes, but you switched to statistical mechanics, and so did I
> Having done so, we can write down whatever body of laws we choose to
> describe behaviour.
You are not doing that on your website, where you follow an axiomatic
way, so don't claim it for other branches (because you don't know an
axiomatic way and are unwilling to learn one)
...
Unfortunately, you have, again, steered the discussion to a dead end.
As before, I will not reply in case you will comment on this posting -
right is not automatically who has the last word
Best wishes,
Peter
Oh No
>Oh No wrote on Thu, 23 Apr 2009 04:56:27 -0600:
>
>(...)
>
>>> >since
>>> >"It is impossible that two bodies occupy the same space" (ibid.)
>>>
>>> >The latter principle has been stressed already by Newton (De
>>> >gravitatione...) - since it doesn't play any role for the planetary
>>> >motion, it is not particularly mentioned in the 'Principia'
>>>
>>> sounds like Euler got it wrong, to me.
>>
>>>Euler got the gravitation wrong, but his axiomatics is superior to
>>>Newton's one in that it can be generalized, while Newton's one cannot
>>
>> But the quote above shows he was talking nonsense. Anyway Euler was
>> largely responsible for the Euler-Lagrange equation, and all that
>> nonsense which has so misguided modern investigations in physics.
>
>I have sniped many paragraphs writen in inadequate language and some few
>mistakes. But this part of the message could confound some readers.
>
>Euler may have done mistakes (just as everyone does). However, the Euler-
>Lagrange equations are not nonsense. They are an useful theoretical tool
>for solving problems, and this explain their central role in "modern
>investigations in physics".
>Of course, another issue is if those equations are or not over-
>evaluated by some authors. Personally, I am aware that not any dynamical
>problem can be solved by them. But, I remark again, the Euler-Lagrange
>equations are not nonsense
>
Yes. Of course I exaggerate. The Euler-Lagrange equations are perfectly
correct *equations* when correctly applied and can be used to solve
problems. I am by no means certain that they are ever the best way of
solving problems. In many cases I know that they are not. I refer as
nonsense not to the equations themselves, but to the role in which many
physicists seem to cast them, as some sort of fundamental description of
nature. Equations can be mathematically correct, yet non descriptive in
interpretation.
Oh No
>On 23 Apr., 12:56, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
>> >> >> We need conservation of momentum,
>>
>> >> >yes - does it follow from your proposed definition of CM?
>>
>> >> No. (So far I have only tried to define classical bodies, btw.)
>>
>> >Momentum conservation should be a consequence of the properties of the
>> >bodies - I forsee, that else you will permanently be compelled to add
>> >ad-hoc new postulates.
>>
>> This is nonsense. Momentum conservation is well known to be a
>> consequence of the homogeneity of space.
>
>Below you write that you have to postulate it - such confusion will
>never lead to serious science, I'm afraid to have to say
This is your confusion not mine. I did write that I do not use a
Lagrangian formulation for classical mechanics, therefore I use
conservation of momentum as a postulate. More generally conservation of
momentum can be demonstrated from first principles in relativistic
quantum theory, without reference to a Lagrangian.
>
>As well known, the bodies are supposed to be in spacetime which itself
>is homogeneous and isotropic
Nonetheless momentum conservation is not a property of bodies as you
wrote, but a consequence of the relationship bodies have with spacetime.
>
>> If you introduce ad hoc
>> assumptions which are known to be wrong I foresee that you will
>> permanently be compelled to ignore physics and to fantasise about your
>> own metaphysics.
>
>I regret that you are unable or unwilling to understand even a small
>piece of Euler's approach to CM
I regret that you are not able to understand that momentum cannot be
treated as a property of a body in isolation.
>> >> For
>> >> classical mechanics I would have to take conservation of momentum as a
>> >> fundamental principle, because I don't like the Lagrangian formulation.
>> >> For quantum theory it can be proven,
>>
>> >Perhaps by means of too many assumptions
>>
>> You are the one suggesting an unnecessary, and false, assumption.
>
>My "Perhaps by means of too many assumptions" was in your style of
>adding one unfounded claim after the other, in order to demonstrate
>you that this leads to nothing => you should return to bring forward
>arguments, as (partially) at the beginning of this thread (if not,
>discussion is meaningless)
I have brought forward arguments. Simple, undeniable arguments, but you
ignore them.
>> >> and from there it can be carried
>> >> into the classical domain.
>
>This I'm not denying - but as you switched to gases some postings
>before, I have extended the topic from classical (and quantum) bodies
>to CM
You were then one who wanted to talk of gases.
>
>> >> Just
>> >> as I prefer conservation of momentum as a fundamental principle to
>> >> Newton's laws.
>>
>> >Newton's laws are an unappropriate starting point for constructing CM,
>> >because Law 2 prevents the generalization to other branches.
>>
>> This is nonsense.
>
>Bohr, Heisenberg, Schrödinger are nonsense - sorry, that's not the
>level to discuss at
>
These are the fathers of quantum theory. There is a big difference
between saying that the classical definition of force does not apply in
the quantum domain and saying that if we have a definition of force it
is impossible to develop any other physics. I am quite certain Bohr
Heisenberg and Schrödinger did not say that, but you did. What you said
was nonsense. A definition does not prevent you from doing anything.
>> Newton's laws are the starting point for CM.
>This is nonsense, because there are several starting points possible.
>(BTW, in case you will eventually read it, you will observe that
>Newton's 'Principia' itself doesn't start with the Laws.)
I have read enough to know that I don't agree with your interpretation.
>> To that
>> we may add Maxwell's equations,
>
>As I have foreseen: you add and add and add...
>
>> The Navier-Stokes equation, gas laws
>
>Can probably largely derived (analogously to the Maxwell equations)
Largely, they can. The Navier-Stokes equation in particular can be
understood as a consequence of conservation of momentum. However it is
still necessary to generalise the notion of a classical body to that of
a classical fluid.
>> >> >energy loss at impacts means heat being outside CM
>>
>> >> Yes. So we need this as a fundamental of CM.
>>
>> >one cannot take something as fundamental what is outside :-o
>>
>> Again you are talking nonsense. By your definition there is no classical
>> mechanics, because it can all be bases on things which are outside CM.
>
>It is favourable to command some basic knowledge on elementary logics
>before commenting on elementary conclusions and trying to formulate
>own conclusions ;-)
Yes, I think you should apply that.
>> >> I don't see impenetrability as sufficient for elastic impacts, because
>> >> there are also non-elastic impacts. Something more would be needed.
>>
>> >Having thought about that, I'm not sure, if inelastic impacts cannot
>> >be included, though heat production can be treated only
>> >phenomenologically as an addendum (friction forces etc.)
>>
>> As is so for all of classical mechanics, though as I have said, your use
>> of "phenomentogical" is inappropriate.
>
>There is, perhaps, a difference between the English and German
>understanding of this word
Perhaps. I have suggested empirical.
>> >Impenetrability gives you
>> > d[f(v)v] = 1/m F dt
>>
>> >f(v) describes the dependence of the change of v by F on the current
>> >value of v (Newton and Euler assumed silently f==1) - In principle, F
>> >can be any function of v
>>
>> I don't see where this comes from,
>
>I have derived it earlier in this group)
I do not see that it can be derived from only impenetrability. We also
need conservation of momentum, and then it is not clear the we need
impenetrability.
>
>> but if it is necessary to assume in
>> addition that f==1 then clearly impenetribility on its own gives you
>> nothing much of value.
>
>As I wrote: It is favourable to command some basic knowledge on
>elementary logics before commenting on elementary conclusions and
>trying to formulate own conclusions: I have written, that Newton and
>Euler have silently assumed f==1, ie, v-independent, I have not
>written that this assumption is necessary.
No you haven't, but it is necessary to get the correct definition of
force.
>
>If F depends on v as state variable, as in the magnetic Maxwell-
>Lorentz force, q v x B, f(v) becomes the Lorentz factor.
This is only a minor shift of ground, to make the theory relativistic.
>> >> I would disagree. Seems to me that all classical laws are
>> >> phenomenological as you say, though I would not disparage that and I
>> >> would call them empirical.
>>
>> >No, many laws can be derived from the impenetrability and, hence, are
>> >not "phenomenological", or "empirical".
>>
>> Is not impenetribility empirical.
>
>Yes, in the same sense and extent as Newton's Laws
Then you have no cause to disparage empirical law.
>
>> Anyway, you have just shown that
>> nothing much of interest can be derived from impenetribility.
>
>No, you have shown that you are unable or unwilling to learn what can
>(and what cannot) derived from it, I'm afraid to have to said.
It is obvious that impenetribility is not enough on its own to derive
anything. Have you even dispensed with N1 for your claimed derivation?
>> >Euler got the gravitation wrong, but his axiomatics is superior to
>> >Newton's one in that it can be generalized, while Newton's one cannot
>>
>> But the quote above shows he was talking nonsense.
>
>Again, this is not the level to discuss at
There is not much else one can say about that quote.
>
>> Anyway Euler was
>> largely responsible for the Euler-Lagrange equation, and all that
>> nonsense which has so misguided modern investigations in physics.
>
>This is not only many levels below serious, but so wrong against
>undisputed knowledge, that it even violates our charter, I'm afraid to
>have to say
I have clarified in my answer to Juan.
>> >you wish to have friction from the very beginning, but not gravity :-o
>>
>> I thought the question was to differentiate quantum from classical.
>
>Yes, but you switched to statistical mechanics, and so did I
It was you who switched.
>> Having done so, we can write down whatever body of laws we choose to
>> describe behaviour.
>
>You are not doing that on your website, where you follow an axiomatic
>way, so don't claim it for other branches (because you don't know an
>axiomatic way and are unwilling to learn one)
I thought we were just discussing how to distinguish "classical" from
"quantum".
Peter
>
> >Yes, but you switched to statistical mechanics, and so did I
>
> It was you who switched.
This only demonstrates another time how careless you treat the past
and are ready to claim the opposite of the obvious, see your 1st
answer to my OP:
"Thus spake Peter <end...@dekasges.de>
>Dear all,
>In order to find out, where classical and where quantum statistical
>mechanics apply, we need to find out:
> What is classical - what quantum?
>Let's start with
> What is a classical particle (body) - what a quantum particle?
>I'm quite sure, that the following definition is useful.
> The essence of the classical bodies is their impenetrability.
>(Euler)
We are talking of statistical mechanics, and hence of gases."
Thus, while I had proposed to solve the issue of the relationship
between classical and quantum gases through analysing the relationship
between classical and quantum particles, you have immediately brought
in the issue of gases.
I'm here to discuss scientific ideas, irrespectively of their age or
belonging to schools etc., not for psycho-terror and pride of
ignorance, I'm afraid to have to say.
Best wishes,
Peter
Peter
<juanREM...@canonicalscience.com> wrote:
> Oh No wrote on Thu, 23 Apr 2009 04:56:27 -0600:
>
> (...)
>
> >> >since
> >> >"It is impossible that two bodies occupy the same space" (ibid.)
>
> >> >The latter principle has been stressed already by Newton (De
> >> >gravitatione...) - since it doesn't play any role for the planetary
> >> >motion, it is not particularly mentioned in the 'Principia'
>
> >> sounds like Euler got it wrong, to me.
>
> >>Euler got the gravitation wrong, but his axiomatics is superior to
> >>Newton's one in that it can be generalized, while Newton's one cannot
>
> > But the quote above shows he was talking nonsense. Anyway Euler was
> > largely responsible for the Euler-Lagrange equation, and all that
> > nonsense which has so misguided modern investigations in physics.
>
> I have sniped many paragraphs writen in inadequate language and some few
> mistakes. But this part of the message could confound some readers.
I agree; it's a shame that such claims appear in our group :-((
Euler invented the calculus of variations for the optimization of
curves, possibly stimulated by his activities in the calculation of
ships. The 1st publications were in the 40-ies. This calculus doesn't
play any role in his axiomatic foundation of CM in the
"Anleitung" (around 1750); Maupertuis' principle of least action
(formulated in mathematical form by Euler even before him) is just
mentioned. According to Weizsäcker ('Aufbau der Physik' ?), Euler
considered the description of mechanical motions by means of
variational principles (abused by teleology) and by differential eqs.
(evoked by the defenders of natural causality) to be equivalent.
> Euler may have done mistakes (just as everyone does). However, the Euler-
> Lagrange equations are not nonsense. They are an useful theoretical tool
> for solving problems, and this explain their central role in "modern
> investigations in physics".
I agree
> Of course, another issue is if those equations are or not over-
> evaluated by some authors.
Yes. I consider it to be useful, eg, to vary Lagrangians, in order to
extend existing models, where one can exploit the tight connection
with symmetry. However, I consider it methodologically doubtful to put
a Lagrangian at the front of a branch of physics.
> Personally, I am aware that not any
perhaps, you mean "not every"
> dynamical
> problem can be solved by them. But, I remark again, the Euler-Lagrange
> equations are not nonsense
Thank you,
Peter
Oh No
>On 23 Apr., 17:58, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> ...
>> >> I thought the question was to differentiate quantum from classical.
>>
>> >Yes, but you switched to statistical mechanics, and so did I
>>
>> It was you who switched.
>
>
>This only demonstrates another time how careless you treat the past
>and are ready to claim the opposite of the obvious, see your 1st
>answer to my OP:
>
See your question, in which you asked about classical and quantum
statistical mechanics.
>"Thus spake Peter <end...@dekasges.de>
>
>>Dear all,
>
>>In order to find out, where classical and where quantum statistical
>>mechanics apply, we need to find out:
>
>> What is classical - what quantum?
>
>>Let's start with
>
>> What is a classical particle (body) - what a quantum particle?
>
>>I'm quite sure, that the following definition is useful.
>
>> The essence of the classical bodies is their impenetrability.
>>(Euler)
>
>We are talking of statistical mechanics, and hence of gases."
>
>Thus, while I had proposed to solve the issue of the relationship
>between classical and quantum gases through analysing the relationship
>between classical and quantum particles, you have immediately brought
>in the issue of gases.
As you say, I brought in the issue of gases in response to your question
about gases.
>
>I'm here to discuss scientific ideas, irrespectively of their age or
>belonging to schools etc., not for psycho-terror and pride of
>ignorance, I'm afraid to have to say.
>
I think that when you ask a question, and start making false accusations
because you do not like the scientific answer, then you demonstrate
exactly the opposite.
Oh No
>> Of course, another issue is if those equations are or not over-
>> evaluated by some authors.
>
>Yes. I consider it to be useful, eg, to vary Lagrangians, in order to
>extend existing models, where one can exploit the tight connection with
>symmetry. However, I consider it methodologically doubtful to put a
>Lagrangian at the front of a branch of physics.
>
to as nonsense, not the equations themselves.
Oh No
>On 23 Apr., 17:05, "Juan R." González-Álvarez
><juanREM...@canonicalscience.com> wrote:
>> Oh No wrote on Thu, 23 Apr 2009 04:56:27 -0600:
>>
>> (...)
>>
>> >> >since
>> >> >"It is impossible that two bodies occupy the same space" (ibid.)
>>
>> >> >The latter principle has been stressed already by Newton (De
>> >> >gravitatione...) - since it doesn't play any role for the planetary
>> >> >motion, it is not particularly mentioned in the 'Principia'
>>
>> >> sounds like Euler got it wrong, to me.
>>
>> >>Euler got the gravitation wrong, but his axiomatics is superior to
>> >>Newton's one in that it can be generalized, while Newton's one cannot
>>
>> > But the quote above shows he was talking nonsense. Anyway Euler was
>> > largely responsible for the Euler-Lagrange equation, and all that
>> > nonsense which has so misguided modern investigations in physics.
>>
>> I have sniped many paragraphs writen in inadequate language and some few
>> mistakes. But this part of the message could confound some readers.
>
>I agree; it's a shame that such claims appear in our group :-((
>
>Euler invented the calculus of variations for the optimization of
>curves, possibly stimulated by his activities in the calculation of
>ships.
Doubtless he developed it, but in fact the origin of the calculus of
variations was Newton's solution to the problem of the brachistochrone.
Newton's solution was submitted anonymously. However Johann Bernoulli,
who set the problem, remarked "I recognise the lion by his paw".
Juan R.
(...)
>> Personally, I am aware that not any
>
> perhaps, you mean "not every"
Yes, sorry, this is another instance of what Charles correctly considered
my "extremely poor grasp of the English language."
>> dynamical
>> problem can be solved by them. But, I remark again, the Euler-Lagrange
>> equations are not nonsense
>
> Thank you,
> Peter
Thank you by the correction.