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  #101  
Old April 20th 08 posted to sci.physics.relativity,sci.physics
Thomas Heger[_2_]
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Posts: 468
Default Discussion of Fields


"maxwell" schrieb im Newsbeitrag
...
On Apr 13, 4:39 pm, HW@....(Dr. Henri Wilson) wrote:
Let's be honest. Nothing physics has produced so far has given any insight
into
what makes a 'field'. Apart from the fact that the maths describing the
forces
are well known, action-at-a-distance is as much a mystery as ever.

The reason is, that fields do not mediate anything. It just the way we see
the world. A field is a unit distributing over space, i.e. temperatur in the
sky. The distribution of temperatur is not at all governed by the field. Its
gas that is floating around, heated up, gets cooled and sometimes rains.
In case of charge its more tricky, but its not the field that make the
charges repell. We see something moving and assign the moving to a cause.
But a field is *our* concept, that comes from our view of the world. We may
call it a field, but electrons dont have ears. So we are just gazing at
something moving around.
In case of gravity we have an appropriate concept, that assigns gravity to
the geometry of worldlines. It is a specific view that makes GR unique, it
is observer invariant or maybe observer independent.
With some reason QM can't deal with that. The reason is, that QM rely on
fields, what you can't find in spacetime. Guess whos right.

Thomas Heger

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  #102  
Old April 21st 08 posted to sci.physics.relativity,sci.physics
Dr. Henri Wilson
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Posts: 4,242
Default Discussion of Fields

On Sun, 20 Apr 2008 13:37:06 -0700 (PDT), PD wrote:

On Apr 19, 6:12*pm, HW@....(Dr. Henri Wilson) wrote:
On Fri, 18 Apr 2008 15:47:14 -0700 (PDT), PD wrote:


Of course it's different. They have different measurable effects.
Doesn't mean there's some *stuff* in that space.


I think so.


Yes, I know you think so. It would be good if you could bear out a
model that shows the distinction is due to "stuff" rather than just
having a different property.


That's not to say that Wilson type 2 matter is ruled out.
It's just that Wilson type 2 matter isn't even far enough along as a
model to make the comparison. It is a tiny gnome model -- and gnomes
have got a cute name too.


Nevertheless, Watter is what makes space carrying a field different from
complete emptiness.


OK, if you say so. Nevertheless, until you can make qualitative and
quantitative predictions from Watter, then it's as useless as a screen
door on a submarine.


All the predictions are known.


Work through one quantitative prediction of Watter. Just one.


How about: F = K.q1.q2/d^2


You haven't shown how your model of Watter produces this prediction.


That is the task ahead.

It would be nice, by the way, if your Watter model produced a
prediction that distinguished itself from those already known for what
you call ordinary type 1 matter, especially since Watter is supposed
to be something different, some kind of type 2 matter that is
distinguishable from the other stuff.


Its predictions will be the same as those already known.
The only way to investigate Watter is to start with the known maths and
construct a model that will produce it.

That's how physics works.


Henri Wilson. ASTC,BSc,DSc(T)
www.users.bigpond.com/hewn/index.htm

.....specialising in teaching physics to engineers and mathematicians....
  #103  
Old April 21st 08 posted to sci.physics.relativity,sci.physics
Dr. Henri Wilson
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Default Discussion of Fields

On Sun, 20 Apr 2008 09:12:37 -0700 (PDT), maxwell wrote:

On Apr 13, 4:39*pm, HW@....(Dr. Henri Wilson) wrote:
Let's be honest. Nothing physics has produced so far has given any insight into
what makes a 'field'. Apart from the fact that the maths describing the forces
are well known, action-at-a-distance is as much a mystery as ever.

Consider a completely isolated negative charge in remote space. The question
is, does its 'field' exist in the absence of another charge. If so, how is the
surrounding space modified in such a way that if another charge is introduced
at any distance , a force immediately exists between the two. That force can be
attractive or repulsive depending whether the charges are unlike or like.

The gravitational field associated with unit mass is fundamentally different in
that like masses ATTRACT each other. There is no information about the nature
of forces between positive and 'negative' mass (presumeably anti-matter).
It can be deduced from this that the properties of space that account for an
electrostatic field must be fundamentally different from those that are
associated with gravity.
It is also apparent that the relative movement of a charge or charges somehow
alters their combined surrounding fields to create what is called a magnetic
field. Again, although the maths of magnetism are well documented, there is no
actual physical model that describes the relationship between electrostatic and
magnetic force fields.

A second question asks whether the effect of the field of an individual source
truly extends to infinity according to the inverse square law or it
disintegrates, becomes fragmented and eventually merges with other fields.

Henri Wilson. ASTC,BSc,DSc(T)www.users.bigpond.com/hewn/index.htm

....specialising in teaching physics to engineers and mathematicians....


The following dialogue illustrates the value of open discussion in
newsgroups, such as this one. In trying to clarify the 'field'
concept in the moderated, so-called 'research' newsgroup, Igor
exploited his power as 'moderator' to suppress once again a viewpoint
he fundamentally disagreed with. Since this happens all the time with
'refereed' professional physics journals, it is obvious why physics is
making little progress - particularly when theorists (read
mathematicians) are almost universally obsessed with 'field theory'.


The basic question is, what is 'matter'?
It is just a manifestation of properties of fields? Or are fields the
manifestaions of properties of matter?

Obviously neither answer if forthcoming would be satisfactory. There must be
another, entirely different explanation.....a PHYSICAL ONE.

Once again, Igor, philosophy defeats you. But we can always rely on you
using political power to suppress alternative viewpoints.

On 4/19/08 3:51 PM, "Igor Khavkine" wrote:
Unfortunately, the article you posted to sci.physics.research is
inappropriate for the newsgroup because it is too vague.
Proponents of continuum mathematics love to
confuse the issue of point particles (confirmed by experiment) versus
fields (confirmed by mathematicians, like Igor). Even Fred Hoyle, who
authored books on action-at-a-distance, still wanted to call the
functions on the particle's worldline: 'fields'. As a mathematician
he should have known that mathematical fields are defined everywhere
through space, not just along time-based trajectories. But the
discrete nature of reality keeps sticking its fingers up the noses of
the continuists, who have never accepted the reality of particles;
metaphysically they need to keep the 'plenum' so they can retain 'the
magic of the infinite'. They even have to perform somersaults with
artifacts like the Dirac delta 'function' so that can keep their
differential calculus and match it to the point nature of electrons.
All the great physicists (Newton, Dirac, Feynman) preferred the
particle model to DesCartes' action-filled void.




Henri Wilson. ASTC,BSc,DSc(T)
www.users.bigpond.com/hewn/index.htm

.....specialising in teaching physics to engineers and mathematicians....
  #104  
Old April 21st 08 posted to sci.physics.relativity,sci.physics
PD
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Posts: 22,012
Default Discussion of Fields

On Apr 20, 5:02*pm, HW@....(Dr. Henri Wilson) wrote:

Its predictions will be the same as those already known.
The only way to investigate Watter is to start with the known maths and
construct a model that will produce it.

That's how physics works.


Uh, no, that is not how physics works. A new model gets developed into
*new math* and in particular makes predictions that are *not* made by
theories to date. It is in fact the distinctive predictions of the new
model that make it testable against experiment -- since it makes
claims that are quantitatively *different* than what current models
make, then the measurement of that quantity thereby tells you whether
the new model is right and the current models necessarily wrong, or
vice versa.

THAT is how physics works.

Co-opting the math of a current theory and retaining all of its
predictions and imbuing it with an "alternate explanation" is
decidedly *not* how physics works. That is humbuggery. You can bugger
hums all you like, if that's all you want to do. Just don't pretend
it's doing physics.

PD
  #105  
Old April 21st 08 posted to sci.physics.relativity,sci.physics
Eric Gisse
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Posts: 18,191
Default Discussion of Fields

On Apr 20, 9:55*am, "Thomas Heger" wrote:
I repeat: Tajmar's work was never published. Stop quoting it as if it
proves a point


.
I could show you the exact relation between those terms of electric charge,
rotation of supercooled bodies and gravitation. I don't *think you would
trust me, but maybe you try to understand.


[snip words]

You didn't show anything, you just wrote a lot of words that had no
quantitative predictive ability.
  #106  
Old April 21st 08 posted to sci.physics.relativity,sci.physics
Jan Panteltje
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Posts: 2,591
Default Discussion of Fields

On a sunny day (Mon, 21 Apr 2008 06:51:17 +1000) it happened "Timo A.
Nieminen" wrote in
:

as then I is zero. So enter the electron, and modern electronics.

Calling something "electron" isn't a "mechanism". Or do you think it is?
Given that we don't know what an electron _is_, beyond its measured
properties, all we have is a name and a mathematical model.


It is a step beyond playing just with the basic math that has no physical
way or model, or mechanism, of HOW things happen, what does it.


How is it a "step beyond"? All we have is a mathematical model of
observable effects of electrons. Where is there any hint of "mechanism"?



The electron is the mechanism.
Sounds a bit like the medium is the message... but really, in electronics
all I play with are electrons.
Without the concept of electrons nothing would be comprehensible.
From the math .. forget it, math is an engineering tool to get
quantitives. ;-)


Note also the the mathematical model is mathematically-troubled
( , in both classical and quantum theories).

As in Newton's gravity, as in relativity, where avid mathematicians play endlessly
with some formulas to make time machines, warp drives, what not.
You need a mechanism, for reality, if not only to avoid insane constructs.


No, you need to stay in touch with observation and experiment, basically
remain connected with reality as we measure it. Reality keeps it real, not
some theorised un-measurable "mechanism".


Well, if you wannabee right by saying things your way, or think you say it
better that way, who cares.
Fact remains we have no time machine and no warp drive.
But the mathematicians dreamed up those.
So where is reality? Not with playing with incomplete math.


despite Newton's lack of mechanism?


In the area of what gravity IS, the mechanism, NO.


Why not just answer the question? I'm not asking about the area of "what
gravity IS, the mechanism", I'm asking about physics in general,
especially that part of it that makes use of Newtonian gravity. Did
physics progress, based on Newton's mathematical model of gravity, despite
the lack of mechanism?

If yes, then your original statement about mechanism being needed for
physics to advance was wrong.

If no, then the work of Galilei, Newton, Priestly, Aepinus, etc was not an
advance, and we may as well abandon Newtonianism and go back to mediaeval
physics or earlier.

Is this why you avoid answering it?

We have no anti gravity, we cannot manipulate gravity, or inertia, it
is still a black box.

If you could show a machine that changed gravity, or the weight of an object,
then yes we would have progressed.


That was the answer you asked for...


We can change gravity and weight in the same way that we can change
electric fields, charges, and electric forces. We understand the effects.


No we cannot.


No, you are cheating here, I propose experiments, but the cheaters are soo afraid to
repeat the experiments that falsify their believes (like that ESA experiment).
I do NOT suggest to fiddle with incomplete questionable formulas endlessly,
(like a hundred years with Einstein's).


What experiments? You've proposed none in this thread.


You are getting a bit irritating, and makes one feel like wanting to terminate the exchange,
because I mentioned, and gave a link, to the ESA experiment TWICE.


Why the obsession with Einstein? It's Newtonianism (i.e., mathematical
models, no "mechanism") that you're complaining about. Einstein's theories
of relativity are the closest we've gotten to any "mechanism" for, e.g.,
why light travels at c in free space, gravity, and more. You might not
like geometry as a mechanism, but it's certainly more explanation than,
e.g., Newton's law of universal gravitation.


Mathematical models gives us numerical values, they do not provide a mechanism,
or explain anything.


They use electromagnets to pulse charged particles, push them in such
a sequence that they speed up.
Of course you can use many waves to try to speed up the surfer, but if those
waves (the EM field here) themselves move at c, and grab on to the charged particles via
EM forces, then you cannot move those particles faster then the waves, even if you pulse
faster, or use a stronger EM field.

"Electromagnetics to pulse charged particles" is a very bad description of
how accelerators work.


Electromagnets. Look dude I have worked there, have detailed knowledge about some of the
electronics that drives those electromagnets, beam positioners, and designed some stuff myself.
It is no hocus pocus, all very real, take a hint.


How much do the electromagnets accelerate the particles?


Never more then the EM field, never faster then c.


"EM wave" is not EM field. You can start with a DC field everywhere. Why
should an electron being accelerated by a DC field have to wait for the
field to "move"?


Ask yourself the question, basically 'what is a field'.
Then we are back to the OP.
IF a field is something that moves between say a positive and negative terminal
(as in electrostatic field), how long does it take for the particle in the middle to notice the
forces have changed if you say make the negative pole more negative?
c.


That isn't an answer. Why should an electron being accelerated by a DC
field have to wait for the field to "move"? The DC field is already there.


You avoid what 'field' actually represents.
Imagine, or try to imagine, that electron, between the two electrodes, something
moves it, is it being carried by some sort of stream? Is something streaming?
Clearly if changing potential on one electrode takes time for the field
to adjust, it's effect to reach that electron, then _something_ moves.
So the question is: what makes up that field, what sort of 'mechanism' (of whatever kind)
can we dream up that would explain this?
There were some really nice propositions made in this newsgroup some years ago, but I would
have to look a while to find it.
If something actually moves, then for sure the electron will never move faster then that stream
(stream just a word for the unknown 'it').
What is charge?


We don't have to change it at all. For a uniform field, the force is
constant. This has been used in real particle accelerators (and still is,
and in CRTs, too).


See previous remark.
Sure, the electron accelerates, with constant DC on the electrodes, the issue
is what is its max speed when accelerated by that DC static field, it is c!.


I wouldn't bother trying it this way - an electrostatic accelerator is all
you need, perhaps with a magnetic field to bring the particle back around
for a 2nd, 3rd, 4th, etc kick of acceleration.


Nope, does not work, see previous remark.


Ah! It's OK for Ptolemy to theorise, and get it wrong for 1,000 years, but
not OK for Einstein to theorise, or for "avid mathematicians" to theorise
about FTL space travel, time travel, etc (even though you've stated that
FTL space travel is a worthy goal)?


Look, you theorise all you want, if you got it wrong people will call you,
if you got it right maybe you get a Nobel, theorising is OK.

  #107  
Old April 21st 08 posted to sci.physics.relativity,sci.physics
Thomas Heger[_2_]
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Posts: 468
Default Discussion of Fields


"Eric Gisse" schrieb im Newsbeitrag
...
On Apr 20, 9:55 am, "Thomas Heger" wrote:
I repeat: Tajmar's work was never published. Stop quoting it as if it
proves a point



[snip words]

You didn't show anything, you just wrote a lot of words that had no
quantitative predictive ability.


I predicted that the experiment is working in one direction but not in the
other (and why). To figuere out the effect I would need some kind of tool to
do complex geometry. Its possible but quite difficult. So I'm not shure
being able to provide that calculations. Or maybe I'm just too lazy..

Thomas Heger

  #108  
Old April 21st 08 posted to sci.physics.relativity,sci.physics
Timo A. Nieminen
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Posts: 1,216
Default Discussion of Fields

On Mon, 21 Apr 2008, Jan Panteltje wrote:

Timo wrote:

Calling something "electron" isn't a "mechanism". Or do you think it is?
Given that we don't know what an electron _is_, beyond its measured
properties, all we have is a name and a mathematical model.

It is a step beyond playing just with the basic math that has no physical
way or model, or mechanism, of HOW things happen, what does it.


How is it a "step beyond"? All we have is a mathematical model of
observable effects of electrons. Where is there any hint of "mechanism"?


The electron is the mechanism.


A very poor "mechanism". No better than "field". Worse, even. Why are you
happy with "electron" as "mechanism" but not "field"? (Perhaps a good time
to actually try to define what you mean by "mechanism"?)

Sounds a bit like the medium is the message... but really, in electronics
all I play with are electrons.
Without the concept of electrons nothing would be comprehensible.


Almost all of it would be comprehensible. Electronics has about as much to
do with electrons as photonics has to do with photons. Most of electronics
is about EM waves and EM power going up and down the circuit. This happens
at approx. c, while the electrons move at a few mm/s.

OK, there are all the fun quantum devices, like transistors and diodes (or
vacuum tubes even). But from an electronics perspective, you don't need to
know that, all you need is the black box model of the devices.

From the math .. forget it, math is an engineering tool to get
quantitives. ;-)


Well, yes. Isn't this obvious?

Note also the the mathematical model is mathematically-troubled
( , in both classical and quantum theories).

As in Newton's gravity, as in relativity, where avid mathematicians play endlessly
with some formulas to make time machines, warp drives, what not.
You need a mechanism, for reality, if not only to avoid insane constructs.


No, you need to stay in touch with observation and experiment, basically
remain connected with reality as we measure it. Reality keeps it real, not
some theorised un-measurable "mechanism".


Well, if you wannabee right by saying things your way, or think you say it
better that way, who cares.


Because it's central to your original statement that, in the absence of
"mechanism", physics will not advance? _You_ introduced "mechanism",
didn't, and haven't defined "mechanism" (or "advance"), but appear to
continue to defend your original thesis.

Bottom line" "mechanism", as usually understood, is not reality; it's
beyond reality, beyond experimental verification.

Fact remains we have no time machine and no warp drive.
But the mathematicians dreamed up those.
So where is reality? Not with playing with incomplete math.


So, what is your complaint? Please, be explicit! Are you complaining that
"avid mathematicians" are theorising about "warp drives" (which you've
already indicated is a wonderful and glorious aim)? Or just that the warp
drives don't work in reality? In which case, complain to reality, not the
avid mathematicians.

Seriously, how can you simultaneously complain about the lack of practical
time machines, and theoretical work expended on the theory of time
machines?

despite Newton's lack of mechanism?

In the area of what gravity IS, the mechanism, NO.


Why not just answer the question? I'm not asking about the area of "what
gravity IS, the mechanism", I'm asking about physics in general,
especially that part of it that makes use of Newtonian gravity. Did
physics progress, based on Newton's mathematical model of gravity, despite
the lack of mechanism?

If yes, then your original statement about mechanism being needed for
physics to advance was wrong.

If no, then the work of Galilei, Newton, Priestly, Aepinus, etc was not an
advance, and we may as well abandon Newtonianism and go back to mediaeval
physics or earlier.

Is this why you avoid answering it?

We have no anti gravity, we cannot manipulate gravity, or inertia, it
is still a black box.

If you could show a machine that changed gravity, or the weight of an object,
then yes we would have progressed.


That was the answer you asked for...


Oh? But no sign of a yes or no answer? Please, make it clear!

Why not just answer the question? I'm not asking about the area of "what
gravity IS, the mechanism", I'm asking about physics in general,
especially that part of it that makes use of Newtonian gravity. Did
physics progress, based on Newton's mathematical model of gravity, despite
the lack of mechanism?

If yes, then your original statement about mechanism being needed for
physics to advance was wrong.

If no, then the work of Galilei, Newton, Priestly, Aepinus, etc was not an
advance, and we may as well abandon Newtonianism and go back to mediaeval
physics or earlier.

We can change gravity and weight in the same way that we can change
electric fields, charges, and electric forces. We understand the effects.


No we cannot.


Oh? We don't understand the effects? Where then is the (classical) defect
in classical EM field theory? Note that I'm not claiming that we
understand _why_, but merely that we understand the effects. I.e., that we
know what the mathematical model predicts.

No, you are cheating here, I propose experiments, but the cheaters are soo afraid to
repeat the experiments that falsify their believes (like that ESA experiment).
I do NOT suggest to fiddle with incomplete questionable formulas endlessly,
(like a hundred years with Einstein's).


What experiments? You've proposed none in this thread.


You are getting a bit irritating, and makes one feel like wanting to terminate the exchange,
because I mentioned, and gave a link, to the ESA experiment TWICE.


Mentioning != proposing. And the original mention was tangential to the
topic. Will look if time permits. In any case, it's doubly irrelevant,
since this looked like just more of your anti-relativity bugbear,
fundamentally nothing to do with mechanism vs no-mechanism, the foundation
of Newtonianism.

Why the obsession with Einstein? It's Newtonianism (i.e., mathematical
models, no "mechanism") that you're complaining about. Einstein's theories
of relativity are the closest we've gotten to any "mechanism" for, e.g.,
why light travels at c in free space, gravity, and more. You might not
like geometry as a mechanism, but it's certainly more explanation than,
e.g., Newton's law of universal gravitation.


Mathematical models gives us numerical values, they do not provide a mechanism,
or explain anything.


Of course. But a non-answer to the question.

They use electromagnets to pulse charged particles, push them in such
a sequence that they speed up.
Of course you can use many waves to try to speed up the surfer, but if those
waves (the EM field here) themselves move at c, and grab on to the charged particles via
EM forces, then you cannot move those particles faster then the waves, even if you pulse
faster, or use a stronger EM field.

"Electromagnetics to pulse charged particles" is a very bad description of
how accelerators work.

Electromagnets. Look dude I have worked there, have detailed knowledge about some of the
electronics that drives those electromagnets, beam positioners, and designed some stuff myself.
It is no hocus pocus, all very real, take a hint.


How much do the electromagnets accelerate the particles?


Never more then the EM field, never faster then c.


By how much do the _electromagnets_ increase the speed of the particles?

"EM wave" is not EM field. You can start with a DC field everywhere. Why
should an electron being accelerated by a DC field have to wait for the
field to "move"?

Ask yourself the question, basically 'what is a field'.
Then we are back to the OP.
IF a field is something that moves between say a positive and negative terminal
(as in electrostatic field), how long does it take for the particle in the middle to notice the
forces have changed if you say make the negative pole more negative?
c.


That isn't an answer. Why should an electron being accelerated by a DC
field have to wait for the field to "move"? The DC field is already there.


You avoid what 'field' actually represents.
Imagine, or try to imagine, that electron, between the two electrodes, something
moves it, is it being carried by some sort of stream? Is something streaming?


Oh? Are you saying that Coulomb's law doesn't work? That we need to modify
the mathematical model to account for something "streaming" from one
electrode to the other?

Clearly if changing potential on one electrode takes time for the field
to adjust, it's effect to reach that electron, then _something_ moves.


Why? Be careful to define "thing" beforehand! Are you trying to say that
F=Eq is wrong?

So the question is: what makes up that field, what sort of 'mechanism' (of whatever kind)
can we dream up that would explain this?
There were some really nice propositions made in this newsgroup some years ago, but I would
have to look a while to find it.


Unless the "mechanism", the explanation is experimentally/measurably
accessible, then it isn't very useful.

Various suggestions have been made (even coming out of conventional
fundamental theoretical physics) as to mechanism, but they haven't gotten
that much attention, since in the absence of experimental verification,
such is largely metaphysical speculation.

If something actually moves, then for sure the electron will never move faster then that stream
(stream just a word for the unknown 'it').
What is charge?


We don't have to change it at all. For a uniform field, the force is
constant. This has been used in real particle accelerators (and still is,
and in CRTs, too).


See previous remark.
Sure, the electron accelerates, with constant DC on the electrodes, the issue
is what is its max speed when accelerated by that DC static field, it is c!.


Why is this an issue? We already have a good model of why this happens.

--
Timo

  #109  
Old April 21st 08 posted to sci.physics.relativity,sci.physics
PD
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Posts: 22,012
Default Discussion of Fields

On Apr 21, 4:00*pm, "Timo A. Nieminen" wrote:
On Mon, 21 Apr 2008, Jan Panteltje wrote:
Timo wrote:



How is it a "step beyond"? All we have is a mathematical model of
observable effects of electrons. Where is there any hint of "mechanism"?


The electron is the mechanism.


A very poor "mechanism". No better than "field". Worse, even. Why are you
happy with "electron" as "mechanism" but not "field"? (Perhaps a good time
to actually try to define what you mean by "mechanism"?)


In fact, I would challenge Jan to characterize an electron in such a
way that distinguishes it from a field. What are the properties of an
electron that make it more "real" than a field? Be very careful with
the answer, Jan.

PD
  #110  
Old April 22nd 08 posted to sci.physics.relativity,sci.physics
Dr. Henri Wilson
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Posts: 4,242
Default Discussion of Fields

On Mon, 21 Apr 2008 14:25:41 -0700 (PDT), PD wrote:

On Apr 21, 4:00*pm, "Timo A. Nieminen" wrote:
On Mon, 21 Apr 2008, Jan Panteltje wrote:
Timo wrote:



How is it a "step beyond"? All we have is a mathematical model of
observable effects of electrons. Where is there any hint of "mechanism"?


The electron is the mechanism.


A very poor "mechanism". No better than "field". Worse, even. Why are you
happy with "electron" as "mechanism" but not "field"? (Perhaps a good time
to actually try to define what you mean by "mechanism"?)


In fact, I would challenge Jan to characterize an electron in such a
way that distinguishes it from a field. What are the properties of an
electron that make it more "real" than a field? Be very careful with
the answer, Jan.


You relativists really are a primative lot. You are stuck on the bottom rung of
physics and can't raise your tiny little minds above it.

The point is, there is an obvious link between 'matter', 'charge' and 'field'.
The mathematics is well known.
Jan and I wish to speculate on the physics of that link.




PD




Henri Wilson. ASTC,BSc,DSc(T)
www.users.bigpond.com/hewn/index.htm

.....specialising in teaching physics to engineers and mathematicians....
 




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