The nature of Maxwellian physical reality & singularities
Mountain Man
The following quote represents the last paragraph of a paper
delivered by Albert Einstein on the occassion of the centenary
of Maxwell's birth [1931]. For those interested, the complete
article (and thus the context) is available at:
http://magna.com.au/~prfbrown/aether_2.html
"I am inclined to think that physicists will not be satisfied
in the long run with this kind [QM] of indirect description of
reality, even if an adaptation of the theory to the demand of
general relativity can be achieved in a satisfactory way.
Then they must surely be brought back to the attempt to realise
the programme which may suitably be designated as Maxwellian:
a description of physical reality in terms of fields which
satisfy partial differential equations in a way that is free
from singularities."
I do not understand the implications of the final sentence.
What is meant by the statement "fields which satisfy partial
differential equations in a way that is free from singularities".
I would appreciate any summary of this condition.
Many thanks in advance,
Pete Brown
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Our ear for music, our eye for art carry us back to the
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plants, or some sunrise or sunset glow in the distant
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it forth from the deep chambers and set it panting and
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mind there is no peace like nature's, for the wounded
spirit there is no healing like hers. There are indeed
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fly to nature for that silent sympathy and communion which
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precious things in life. Nature is indeed very close to us;
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- From "Holism and Evolution", p.336f
Jan Smuts (South African philosopher-statesman,
father of "Holism", 1870-1950)
http://magna.com.au/~prfbrown/news97_e.html
--------------------------------------------------------------------
Ray Tomes
Mountain Man <prfb...@magna.com.au> in article
<335F4D...@magna.com.au> wrote:
>The following quote represents the last paragraph of a paper
>delivered by Albert Einstein on the occassion of the centenary
>of Maxwell's birth [1931]. For those interested, the complete
>article (and thus the context) is available at:
>http://magna.com.au/~prfbrown/aether_2.html
> "I am inclined to think that physicists will not be satisfied
> in the long run with this kind [QM] of indirect description of
> reality, even if an adaptation of the theory to the demand of
> general relativity can be achieved in a satisfactory way.
> Then they must surely be brought back to the attempt to realise
> the programme which may suitably be designated as Maxwellian:
> a description of physical reality in terms of fields which
> satisfy partial differential equations in a way that is free
> from singularities."
>I do not understand the implications of the final sentence.
>What is meant by the statement "fields which satisfy partial
>differential equations in a way that is free from singularities".
Einstein was very keen on the idea of fields being continuous and the
ultimate description of all matter and energy. I agree with this
philosophical bias.
A partial differential equation just means that the rate of change of
the field with time at every location is linked by equations to the rate
of change of the field (or other related fields) with each spacial
dimension, or often the second differentials are related. Maxwell's
equations are all of this form.
If you have a point charge however it has a singularity at the centre
because as r-->0 then 1/r^2-->infinity. Infinities are a curse.
There are various ways around this sort of thing, and for example you
can have a term like 1/(r^2+a^2) where a is some small constant which
prevents the infinity and allows the field to be continuous everywhere.
The trouble is that so far, an electron shows no signs of such a
variation in its behaviour.
There are people who look for black holes to go to zero gracefully
rather than to minus infinity at the centre. There are some simple
mathematical tricks which can achieve this sort of thing. If a field,
F, has a 1/r^2 behaviour then defining log(f)=F can mean that f is
continuous even though F goes to -infinity.
Exactly this sort of trick gets rid of the infinities in maps at the
poles in a mercurator projection (i.e just make a globe) and Stephen
Hawking has suggested the same trick for getting rid of the big bang
singularity. I prefer the trick of using log(t)=T and making time run
at a regular rate rather than having most of the action at nearly one
point in time.
-- Ray Tomes -- rto...@kcbbs.gen.nz -- Harmonics Theory --
http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm
Etherman
Ray Tomes <rto...@kcbbs.gen.nz> wrote in article
<33643c1d....@aklobs.org.nz>...
> If you have a point charge however it has a singularity at the centre
> because as r-->0 then 1/r^2-->infinity. Infinities are a curse.
There might be a way using distribution theory (the Dirac delta function
is the most famous example of a distribution). In certain integrals that
diverge we can take what's called the Hadamard finite part. I won't
get into the theory here because it's too involved and I'm far from an
expert on the subject. Essentially what is done is to remove the part
of the integral that causes the divergence. It may even be possible to
apply this to QFT and remove the divergences without renormalization.
It may further be possible to remove the divergences from quantum gravity.
--
Etherman
Paul Stowe
In <01bc51c8$e6adf340$0cd3...@etherman.mdc.net> "Etherman" <ethe...@mdc.net>
writes:
I might suggest that the problem is one of viewpoint, not physical reality. A
classic example of this is the flux equation of a "point" radiation source
which is:
S
Fee = ------
4piR^2
Of course as R -> 0, Fee go to infinity. But, knowing that all true
sources (S) occuy a finite real volume (V), we know that:
S = rho V
where rho is a source density. Thus volume is some form of xR^3 and for
a sphere it is 4piR^3/3. Plugging this in we see:
rho[4piR^3] rhoR
Fee = ----------- = ------
12piR^2 3
This then shows us that for any finite source density, as R-> 0 Fee ->
0, not infinity. Same problem, but totally different answers at the
limit. The later matchs observations, while the former is a strict
mathematical interpetation based on, IMHO an invalid assumption.
Paul Stowe
Lawrence Anthony Jones
In message <5jrdfe$3...@sjx-ixn8.ix.netcom.com>
pst...@ix.netcom.com(Paul Stowe) writes:
> S = rho V
> Paul Stowe
Yes, but what is a 'point charge?' Why do we go from charge to
current to 'induced voltage?'(whatever that is). To me, static is
not the same as dynamic. If we adopt the Heaviside view: 'This shall
be reversed', then the idea of currents 'causing' magnetic fields
becomes meaningless. If Heaviside was correct with his idea of
energy current, then it questions the whole existence of electric
charge. However, I do not know how to go about modelling energy
current in a capacitor (energy current holder) when it is not
active. Like most people on the aether debate, I believe that
everything is waves. I can elaborate on this, but what I am trying
to say is difficult to write. Jason Blood says that space is ether
(aether - I even understand this discussion) and I know exactly what
he means. A current must be a displacement of somthing NOT flow of
charge. Perfect space must be straight and is analogous to a uniform
field line of D.
Sorry for digressing from the basic discussion
Lawrence Jones
Lawrence Anthony Jones
> In <01bc51c8$e6adf340$0cd3...@etherman.mdc.net> "Etherman"
<ethe...@mdc.net>
> writes:
> >
> >
> >
> >Ray Tomes <rto...@kcbbs.gen.nz> wrote in article
> ><33643c1d....@aklobs.org.nz>...
> >> If you have a point charge however it has a singularity at the centre
> >> because as r-->0 then 1/r^2-->infinity. Infinities are a curse.
> >
> >There might be a way using distribution theory (the Dirac delta function
> >is the most famous example of a distribution). In certain integrals that
> >diverge we can take what's called the Hadamard finite part. I won't
> >get into the theory here because it's too involved and I'm far from an
> >expert on the subject. Essentially what is done is to remove the part
> >of the integral that causes the divergence. It may even be possible to
> >apply this to QFT and remove the divergences without renormalization.
> >It may further be possible to remove the divergences from quantum gravity.
> >
Paul Stowe replied
> I might suggest that the problem is one of viewpoint, not physical
reality. A
> classic example of this is the flux equation of a "point" radiation source
> which is:
> S
> Fee = ------
> 4piR^2
> Of course as R -> 0, Fee go to infinity. But, knowing that all true
> sources (S) occuy a finite real volume (V), we know that:
> S = rho V
> where rho is a source density. Thus volume is some form of xR^3 and for
> a sphere it is 4piR^3/3. Plugging this in we see:
> rho[4piR^3] rhoR
> Fee = ----------- = ------
> 12piR^2 3
> This then shows us that for any finite source density, as R-> 0 Fee ->
> 0, not infinity. Same problem, but totally different answers at the
> limit. The later matchs observations, while the former is a strict
> mathematical interpetation based on, IMHO an invalid assumption.
> Paul Stowe
My problem is:'what is a point charge?' It puzzles me that Maxwell
did not seem to ask more questions about the nature of electric
charge once he discovered Displacement Current. Why do we always go
from charge to current to 'induced voltage?' (whatever that is).
Heaviside said:'this shall be reversed' and no longer accepted that a
current 'caused' a magnetic field. He regarded the magnetic field as
the active side of what he termed Energy Current. I assume that
Energy Current in its passive state is what we are all calling the
ether (or aether - I understood this little debate a while ago).
However, my major problem is how one models enrgy current in a
capacitor without resorting to charge and displacement current. For
example, if a 'charged' capacitor is connected to an uncharged
capacitor, then I cannot fathom how these closed loops of Energy
Current would be redistributed to the new capacitor. I often wonder
why so many people seem to believe that static is the same as dynamic.
Sorry to have digressed from your original arguement. I am just
determined to find out what the ehter really is. Wave particle
duality troubles me so much - if the ether is always being displaced,
then I have to assume that it is displaced forever (forever is a
closed circular word). But I think everyone should realise that
charge does not flow: only currents flow. And currents cannot,in
practice, be integrated. A wave is, by definition, temporal. It
does not have a begining nor an end. The words begining and end are
spatial words. Perfect space (if it existed) must be straight and
instantaneous. Jason Blood once stated that the ether is space - I
think I understood what he meant in this statement.
Lawrence Jones
Paul Stowe
In <199704261...@zetnet.co.uk> Lawrence Anthony Jones
I might suggest that the problem is one of viewpoint, not
physical reality. A classic example of this is the flux
equation of a "point" radiation source which is:
S
Fee = ------
4piR^2
Of course as R -> 0, Fee go to infinity. But, knowing that all
true sources (S) occupy a finite real volume (V), we know that:
S = rho V
where rho is a source density. Thus volume is some form of xR^3
and for a sphere it is 4piR^3/3. Plugging this in we see:
rho[4piR^3] rhoR
Fee = ----------- = ------
12piR^2 3
This then shows us that for any finite source density, as R-> 0
Fee -> 0, not infinity. Same problem, but totally different
answers at the limit. The later matches observations, while the
former is a strict mathematical interpretation based on, IMHO an
invalid assumption.
Paul Stowe
My problem is:'what is a point charge?'
Strictly speaking there are no point charges. I think even the most
diehard modernist accepts this as a definition.
It puzzles me that Maxwell did not seem to ask more questions
about the nature of electric charge once he discovered
Displacement Current. Why do we always go from charge to current
to 'induced voltage?' (whatever that is). Heaviside said:'this
shall be reversed' and no longer accepted that a current 'caused'
a magnetic field. He regarded the magnetic field as the active
side of what he termed Energy Current. I assume that Energy
Current in its passive state is what we are all calling the ether
(or aether - I understood this little debate a while ago).
When one dispenses with the physical medium interpretation of space,
there is no way to introduce such things without major hand waving.
Modernist do this by replacing the tradition aether medium with a
space-time continuum, virtual particles, and zero point energy. They
can't deny that, as Maxwell pointed out, space is the seat of real
physical energy and observable processes. So, to account for these one
has to have an aether, or all of these others.
However, my major problem is how one models energy current in a
capacitor without resorting to charge and displacement current.
For example, if a 'charged' capacitor is connected to an
uncharged capacitor, then I cannot fathom how these closed loops
of Energy Current would be redistributed to the new capacitor. I
often wonder Why so many people seem to believe that static is the
same as dynamic. Sorry to have digressed from your original
argument. I am just determined to find out what the ether really
is. Wave particle duality troubles me so much - if the ether is
always being displaced, then I have to assume that it is displaced
forever (forever is a closed circular word). But I think everyone
should realize that charge does not flow: only currents flow. And
currents cannot, in practice, be integrated. A wave is, by
definition, temporal. It does not have a beginning nor an end.
The words beginning and end are spatial words. Perfect space (if
it existed) must be straight and instantaneous. Jason Blood once
stated that the ether is space - I think I understood what he
meant in this statement.
Lawrence Jones
A little history of Maxwell's work. Maxwell fully acknowledges that
his Treatise's were, of necessity, incomplete (or as he phrased it: "in
our current state of ignorance"). He take the classical simplification
of assuming an incompressible medium. This is done because it
significantly simplifies the resulting derivations, and unless the
media departs significantly from its equilibrium density, such
compressibility has very little (negligible) impact on the results
under consideration. But compressibility does affect the basic
properties. Assumption of incompressibility mathematically defines the
divergence of field velocity v as:
Div v = 0
where v is the media's particulate velocity. A direct consequence of
this definition is that waves cannot be created or propagated in such a
system (wave speed is infinite). But, as we all know, even though we
assume incompressibility, every media (even liquids and solids) are not
incompressible. The consequence of this is, for field velocity v:
Div v > 0
Thus the momentum field property (p = mv) is
Div p > 0
This has measurable physical consequences, and IS A FUNDAMENTAL
UNIQUE PROPERTY of the field! Given that divergence is defined as:
/ dA (A is area)
Div = Lim V -> 0 <|> --------
/ deltaV
and has physical units of inverse distance (meters), Div v become the
measure of an oscillation in the velocity field at any point in the
continuum. The resulting momentum fluctuation is ... elemental charge,
a unique property that is a consequence of the field's compressibility.
Later,
Paul Stowe
Paul Stowe
S = rho V
Paul Stowe
Lawrence Jones
Div v = 0
Div v > 0
Div p > 0
/ dA
Lawrence Anthony Jones
In message <5jtj4b$7...@sjx-ixn6.ix.netcom.com>
pst...@ix.netcom.com(Paul Stowe) writes:
> Path:
zetnet.co.uk!disgorge.news.demon.net!demon!dispatch.news.demon.net!demon!fido.ne
ws.demon.net!demon!sun4nl!EU.net!news-peer.sprintlink.net!news.sprintlink.net!sp
rint!ix.netcom.com!news
> From: pst...@ix.netcom.com(Paul Stowe)
> Newsgroups: alt.sci.physics.new-theories
> Subject: Re: The nature of Maxwellian physical reality & singularities
> Date: 26 Apr 1997 18:56:11 GMT
> Organization: Netcom
> Message-ID: <5jtj4b$7...@sjx-ixn6.ix.netcom.com>
> References: <199704261...@zetnet.co.uk>
> NNTP-Posting-Host: val-ca3-31.ix.netcom.com
> X-NETCOM-Date: Sat Apr 26 11:56:11 AM PDT 1997
> Lines: 117
> Xref: zetnet.co.uk alt.sci.physics.new-theories:45019
> S = rho V
> Paul Stowe
> Lawrence Jones
> Div v = 0
> Div v > 0
> Div p > 0
> Later,
> Paul Stowe
Lawrence Jones replies:
But in view of the fact that Maxwell did assume that his medium was
incompressible, then I don't know how he arrived at the concept of
displacement current in the first place, when it would have meant an
infinite propogaton velocity. A uniform field cannot change with
time which is why I say that it is analogous to perfect space. If I
calculate the magnetic field at the edge of a capacitor plate that is
being slowly discharged, I can either use Bio-savat or Maxwell's 2nd equation:
non-uniform
Line of dD/dT (mysteriously
transforms A into D when it
terminates on the A
plate)
A
c -*--*--*--*-
P * * * * Lines of D between plate
d -*--*--*--*-
The radius of the plate is R and the distance of separation is d.
The capacitor is slowly discharged at R/2 between c & d.
Hence 2piRH= I - I (1 - d/2R)
And H=Id/4piR^2 (see Am. J. Phys. (1963): 31, 201) for more discussion
I am not a physicist, but in all this ether debate, I keep asking
myself what space really is. Why, for example, do we assume that a
particle has more physical reality than a wave? When I said that
space was analogous to D, I said this because I had to try to imply
temporal independence. And the only way that I could create perfect
space (i.e. convert all my dD/dt into D would be by shorting the
capacitor plates together. I would then conclude that space must be
a condition of complete fullness. I say this because electric charge
is analogus to space. But I run into deep water here because if
(say) I had a charged sphere and was able to insert it into a larger
sphere and allow it to fall inside the larger sphere, then by Gauss's
law the charge on the outside of the large sphere would equal the
charge on the little sphere. However, since the little sphere is in
motion, then it is, by definition, a conduction current. However
inside the sphere, there will be an increasing and a decreasing
dE/dt, so a magnetic field will not be detected. We then conclude
that electric charge cannot change with time. However since charge
is analogous to space I would then conclude that space cannot change
with time. This makes sense to me because change cannot be treated
in a spatial manner. Change forbids the use of spatial words
(begining and end) and exists forever. Forever is a circular word.
This is why I say that that Heaviside's energy current must be the
true displacement current and this srictly forbids any reference to
electric charge. (but I still use it in calculations!!!)
Lawrence Jones
Etherman
Paul Stowe <pst...@ix.netcom.com> wrote in article
<5jrdfe$3...@sjx-ixn8.ix.netcom.com>...
> I might suggest that the problem is one of viewpoint, not physical
reality. A
> classic example of this is the flux equation of a "point" radiation
source
> which is:
>
> S
> Fee = ------
> 4piR^2
>
> Of course as R -> 0, Fee go to infinity. But, knowing that all true
> sources (S) occuy a finite real volume (V), we know that:
>
> S = rho V
>
> where rho is a source density. Thus volume is some form of xR^3 and for
> a sphere it is 4piR^3/3. Plugging this in we see:
>
> rho[4piR^3] rhoR
> Fee = ----------- = ------
> 12piR^2 3
>
> This then shows us that for any finite source density, as R-> 0 Fee ->
> 0, not infinity. Same problem, but totally different answers at the
> limit. The later matchs observations, while the former is a strict
> mathematical interpetation based on, IMHO an invalid assumption.
>
> Paul Stowe
The obvious question is, how do we know the sources have a nonzero
volume?
--
Etherman
john baez
In article <01bc51c8$e6adf340$0cd3...@etherman.mdc.net>,
Etherman <ethe...@mdc.net> wrote:
>In certain integrals that
>diverge we can take what's called the Hadamard finite part. I won't
>get into the theory here because it's too involved and I'm far from an
>expert on the subject. Essentially what is done is to remove the part
>of the integral that causes the divergence. It may even be possible to
>apply this to QFT and remove the divergences without renormalization.
Actually renormalization is just a way of thinking about this process
of extracting the finite part --- see G. Scharf's textbook "Finite Quantum
Electrodynamics". As he notes: "We only try to shake the dogma that
renormalization is essential for understanding the foundations of field
theory. What is essential is the correct manipulation of distributions.
In fact, we find in our causal approach that *the ultraviolet problem is
a consequence of incorrect splitting of distributions. The correct
distribution splitting immediately gives the right finite ("renormalized")
results.*"
>It may further be possible to remove the divergences from quantum gravity.
Not so easy. For a theory to be renormalizable means precisely that
one can extract the finite part in a reasonable way. Perturbative
quantum gravity isn't renormalizable, which means one can't do this.
"The sun's not eternal. That's why there's the blues" --- Allen Ginsberg
me...@cars3.uchicago.edu
within the source's volume.
Mati Meron | "When you argue with a fool,
me...@cars.uchicago.edu | chances are he is doing just the same"
Etherman
me...@cars3.uchicago.edu wrote in article
<E9BC5...@midway.uchicago.edu>...
That's only half an answer. It's the half that we already know.
--
Etherman
Paul Stowe
Paul Stowe Wrote:
Div v = 0
Div v > 0
Div p > 0
Later,
Paul Stowe
Lawrence Jones replied:
But in view of the fact that Maxwell did assume that his medium was
incompressible, then I don't know how he arrived at the concept of
displacement current in the first place, when it would have meant an
infinite propagation velocity.
No, wave velocity does not directly enter into the specific definitions.
A uniform field cannot change with time which is why I say that it is
analogous to perfect space. If I calculate the magnetic field at the
edge of a capacitor plate that is being slowly discharged, I can either
use Bio-savat or Maxwell's 2nd equation:
non-uniform Line of dD/dT (mysteriously transforms
A into D when it terminates on the A plate)
A
c -*--*--*--*-
P * * * * Lines of D between plate
d -*--*--*--*-
The radius of the plate is R and the distance of separation is d.
The capacitor is slowly discharged at R/2 between c & d.
Hence 2piRH= I - I (1 - d/2R)
And H=Id/4piR^2 (see Am. J. Phys. (1963): 31, 201) for more
discussion
I am not a physicist, but in all this ether debate, I keep asking
myself what space really is.
Why, for example, do we assume that a particle has more physical
reality than a wave?
I don't, and don't think most physicist do.
When I said that space was analogous to D, I said this because I had
to try to imply temporal independence.
Why?
And the only way that I could create perfect space (i.e. convert all my
dD/dt into D would be by shorting the capacitor plates together. I
would then conclude that space must be a condition of complete
fullness. I say this because electric charge is analogous to space.
But I run into deep water here because if (say) I had a charged sphere
and was able to insert it into a larger sphere and allow it to fall
inside the larger sphere, then by Gauss's law the charge on the outside
of the large sphere would equal the charge on the little sphere.
However, since the little sphere is in motion, then it is, by
definition, a conduction current. However inside the sphere, there
will be an increasing and a decreasing dE/dt, so a magnetic field will
not be detected. We then conclude that electric charge cannot change
with time. However since charge is analogous to space I would then
conclude that space cannot change with time. This makes sense to me
because change cannot be treated in a spatial manner. Change forbids
the use of spatial words (begining and end) and exists forever.
Forever is a circular word.
This is why I say that that Heaviside's energy current must be the
true displacement current and this strictly forbids any reference to
electric charge. (but I still use it in calculations!!!)
Lawrence Jones
No, you must understand what the "displacement current" D represents in
terms of Maxwell's model. Well what is a current? A current in terms of
field properties is the net directional flow of a physical property (such as
a thermal current, a river ...etc.). So we should interpret the displacement
current to be a measure of the flow of something. As used by Maxwell's
equations D is the measure of the electrical charge per unit area I.E.:
Q / Coulombs \
D = -------- | ---------|
4piR^2 \ m^2 /
of course the better equation is :
rho_Q R
D = -------------
3
We find that D is also defined as:
D = epsilon E
with E being the electric field intensity.
However, where is the flow? The answer lies in the definition of charge
as Div p, as discussed previously. This give coulombs units of Kg/sec.
The "displacement current" then has standard flux units for mass flow
(Kg/m^2-sec) and represents the net cross-sectional field flow at the point
and time of the evaluation.
E (electric field intensity) is the drift velocity of the field at the point
of definition. So what is "drift velocity"? The drift velocity is a direct
measure of the departure from isotropic, and is the velocity vector resulting
from summing all the media particle's velocity vectors at the point of
interest. Of course if E is zero, D is also zero. We find that epsilon then
becomes a standard density term (kg/m^3). We resolve all of Maxwell's EM
units into standard fluid dynamical terminology, which provide a most useful
conceptual picture.
Later,
Paul Stowe
me...@cars3.uchicago.edu
answer you need. Now, what else you're after.
Brian J Flanagan
On 27 Apr 1997, john baez wrote:
>
> In article <01bc51c8$e6adf340$0cd3...@etherman.mdc.net>,
> Etherman <ethe...@mdc.net> wrote:
> >In certain integrals that
> >diverge we can take what's called the Hadamard finite part. I won't
> >get into the theory here because it's too involved and I'm far from an
> >expert on the subject. Essentially what is done is to remove the part
> >of the integral that causes the divergence. It may even be possible to
> >apply this to QFT and remove the divergences without renormalization.
>
> Actually renormalization is just a way of thinking about this process
> of extracting the finite part --- see G. Scharf's textbook "Finite Quantum
> Electrodynamics". As he notes: "We only try to shake the dogma that
> renormalization is essential for understanding the foundations of field
> theory. What is essential is the correct manipulation of distributions.
> In fact, we find in our causal approach that *the ultraviolet problem is
> a consequence of incorrect splitting of distributions. The correct
> distribution splitting immediately gives the right finite ("renormalized")
> results.*"
BJ: How could we conjure you to tell us more? This sounds quite interesting.
Mike Armstrong
> rho[4piR^3] rhoR
> Fee = ----------- = ------
> 12piR^2 3
>
>This then shows us that for any finite source density, as R-> 0 Fee ->
>0, not infinity. Same problem, but totally different answers at the
>limit. The later matchs observations, while the former is a strict
>mathematical interpetation based on, IMHO an invalid assumption.
>
>Paul Stowe
Sorry to butt in, but I have a couple of questions: 1) The source goes
to zero in the above, also. Wouldn't you expect the field to go to zero
regardless of the field distribution around the source point? I think a
better way to illustrate this would be to consider a finite charge
on a conducting sphere, where the discontinuities are easy to see, but
you don't have to deal with anything going to infinity. 2) Which
observations do the finite density assumptions match? If, for instance,
you can only establish an upper limit for the size of an electron
(limited by the resolution of your detector), how can you say for sure
that it's not a point source? I am certainly quite ignorant of current
estimated electron sizes, but I didn't think a lower limit had been
measured.
Mike
(no sig)
mahipa...@orbital.fsd.com
In article <01bc5325$90b66860$09d3...@etherman.mdc.net>,
"Etherman" <ethe...@mdc.net> wrote:
> The obvious question is, how do we know the sources have a nonzero
> volume?
Quite as obviously, if the sources had a *zero volume* they wouldn't
actually exist.
Mahipal |meforce> http://www.geocities.com/Athens/3178/
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Paul Stowe
In <E9Cs3...@info.physics.utoronto.ca> roa...@lphys.chem.utoronto.ca
Your not butting in, consider the fact that any physical property
distributed on zero volume is what? The answer, as indicated, is
nothing, it can't/doesn't exist.
Paul Stowe
Etherman
john baez <ba...@math.ucr.edu> wrote in article
<5k0ccc$q...@charity.ucr.edu>...
> >It may further be possible to remove the divergences from quantum
gravity.
>
> Not so easy. For a theory to be renormalizable means precisely that
> one can extract the finite part in a reasonable way. Perturbative
> quantum gravity isn't renormalizable, which means one can't do this.
I'm not a big fan of perturbation theory. It assumes that the series
is strongly convergent and that the perturbed Hamiltonian has the
same number of eingenvectors as the unperterbed Hamiltonian.
Both assumptions are a bit shaky.
--
Etherman
Mike Armstrong
In article <5k62id$l...@sjx-ixn6.ix.netcom.com>, pst...@ix.netcom.com(Paul Stowe) says:
>
>>that it's not a point source? I am certainly quite ignorant of current
>>estimated electron sizes, but I didn't think a lower limit had been
>>measured.
>>
>>Mike
>
>Your not butting in, consider the fact that any physical property
>distributed on zero volume is what? The answer, as indicated, is
>nothing, it can't/doesn't exist.
>
>Paul Stowe
I agree that the concept of a point charge may be an approximation. What
I wanted to know was if there's a reason to dismiss it that's supported
by an actual experiment, instead of your intuition or a theoretical
difficulty like renormalization problems. The concept of space itself
is, after all, only a model, so what makes a point charge so impossible
(within that model)?
Forgive my devil's advocatism; I was mainly wondering if a lower limit to
the electron's size had actually been established. Anybody know this?
Mike
(no sig)
john baez
In article <01bc5658$75dc1680$28d3...@etherman.mdc.net>,
Actually perturbation series for interesting physics problems
are hardly ever convergent; this has been shown in many specific
cases. People who are serious about rigor usually do perturbation
theory without the assumption of convergence, since there is a lot
you can do with power series that are merely asymptotic (i.e., not
convergent, but close). A good place to read about this is
"Analysis of Operators" by Reed and Simon.
The only reason I brought up perturbation theory is that your comment
about "divergences in quantum gravity" seemed to be referring to
perturbation theory. It's only in perturbative quantum gravity that
anyone has ever obtained any divergences, so it's only in perturbative
quantum gravity that one worries about removing them. The hope of people
working on nonperturbative quantum gravity is that these divergences
are just an artifact of going about things wrongly: pretending that
quantum gravity acts as just a "small perturbation" of flat spacetime,
even at small distance scales.
Etherman
john baez <ba...@math.ucr.edu> wrote in article
<5kip82$2...@charity.ucr.edu>...
> The only reason I brought up perturbation theory is that your comment
> about "divergences in quantum gravity" seemed to be referring to
> perturbation theory. It's only in perturbative quantum gravity that
> anyone has ever obtained any divergences, so it's only in perturbative
> quantum gravity that one worries about removing them. The hope of people
> working on nonperturbative quantum gravity is that these divergences
> are just an artifact of going about things wrongly: pretending that
> quantum gravity acts as just a "small perturbation" of flat spacetime,
> even at small distance scales.
Since I know next to nothing about quantum gravity I didn't know this.
So it seems that physicists shouldn't be wasting their time with
perturbative quantum gravity.
--
Etherman
john baez
In article <01bc5a8d$96186140$45d3...@etherman.mdc.net>,
Etherman <ethe...@mdc.net> wrote:
>So it seems that physicists shouldn't be wasting their time with
>perturbative quantum gravity.
Right. They're not, now. There was a lot of work on it from the
1950s to the 1970s. This led to the conclusion that nonperturbative
quantum gravity was nonrenormalizable and that some other idea must
be tried. Now people work on string theory and the loop representation.
Matt McIrvin
Except that before the late 1970s or early 1980s or so, physicists didn't
really understand effective field theory. Since then people learned that
there's nothing particularly wrong with nonrenormalizable field theories.
Indeed, the word "nonrenormalizable" is a misnomer, because you can
renormalize these theories with no trouble. Initially people were scared
off by the infinite multiplication of interaction terms-- they said that
this removed all scientific content from the theory, because it had an
infinite number of free parameters! But if you are in a regime far enough
below the theory's obligatory high-energy cutoff, all but a finite number
of terms will be *small*, and approximate predictions may be extracted in
the usual manner.
So there has been some work considering perturbative quantum gravity as an
effective field theory. The hope, I guess, is that one might be able to
calculate the incipient effects of gravity's quantum-ness at lower energy
scales than the Planck scale, where they ought to get really big.
Of course, this won't tell you much about what happens at and beyond the
Planck scale, where the effective theory breaks down. And that is where
the other approaches come in.
--
Font-o-Meter! Proportional Monospaced
^
http://world.std.com/~mmcirvin/
Matt McIrvin
In article <mmcirvin-100...@ppp0a008.std.com>,
mmci...@world.std.com (Matt McIrvin) wrote:
> Initially people were scared
> off by the infinite multiplication of interaction terms--
By the way, here I mean "multiplication" in the rabbit sense.
Dan Evens
Matt McIrvin wrote:
> So there has been some work considering perturbative quantum gravity as an
> effective field theory. The hope, I guess, is that one might be able to
> calculate the incipient effects of gravity's quantum-ness at lower energy
> scales than the Planck scale, where they ought to get really big.
>
> Of course, this won't tell you much about what happens at and beyond the
> Planck scale, where the effective theory breaks down. And that is where
> the other approaches come in.
And one can, with a fair amount of justification, claim that what
happens at the Planck scale has not been probed by experiment, and
so we don't care what the theory says happens there. Provided of course
that it says something that has at least a vague hope of actually being
true. Or can be made to have such, through some such adjustment as
renormalization or some similar scheme.
--
Standard disclaimers apply.
I don't buy from people who advertise by e-mail.
I don't buy from their ISPs.
Dan Evens