what is the width of a single photon?

RolandRB

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Jan 18, 2007, 7:05:24 AM1/18/07

to

Let's say for just the sodium yellow line. What would the width of a
single photon and what is its length?

I've tried doing a search and the amount of waffle is staggering. There
must be a straight and simple answer to this. Surely, somebody knows.

Mr. CaN

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Jan 18, 2007, 8:20:08 AM1/18/07

to

I'm not sure anyone does know for sure. You can be certain that the
maximum the width can be is the wavelength. Beyond that I can't help.

Mr. CaN
www.cymek.com
The Singularity Podcast

Andy Resnick

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Jan 18, 2007, 8:38:51 AM1/18/07

to

RolandRB wrote:

> Let's say for just the sodium yellow line. What would the width of a
> single photon and what is its length?

A single photon of definite energy E = hv exists at zero spectral width,
and infinite spatial and temporal extent.

Coherent collections of photons, which together have a finite spectral
width and originate from a finite-sized source, exist in a finite
temporal pulse over a finite spatial extent. The pulse time is
inversely proportional to the spectral width. The smallest focal spot
that can be acheived by a lens with numberical aperture NA is
approximately l/NA, where l is the (mean) wavelength, and that is a very
loose approximation.

>
> I've tried doing a search and the amount of waffle is staggering. There
> must be a straight and simple answer to this. Surely, somebody knows.
>

--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University

Richard Herring

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Jan 18, 2007, 8:41:00 AM1/18/07

to

In message <1169121923....@l53g2000cwa.googlegroups.com>,
RolandRB <rolan...@hotmail.com> writes

That's because without much more qualification it's a meaningless
concept. How, even in principle, could you measure it?

>Surely, somebody knows.
>

--
Richard Herring

WaveMechanic

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Jan 18, 2007, 9:09:57 AM1/18/07

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"RolandRB" <rolan...@hotmail.com> wrote in message news:1169121923....@l53g2000cwa.googlegroups.com...

A photon is a quantum of energy. In lifting a heavy object off the floor and placing it upon the table you do some work, expend some energy. The
object then has the quantity of energy you out into it and can fall on your
toe and break it. Nobody can tell you how wide or what length that energy is.
Mathematical we say E = 1/2mv^2 which depends on the mass and the
velocity, but not the width or length.

Go to the store and buy a 9V battery. Put the terminals on your
tongue, you'll detect a slight tingle. How thick is a tingle?
How long does a banana taste?
What does a metre smell like?
How many tonnes does an apple hear?
How wide is a voltage?
How long is a magnetic field?
It's not a matter of waffling, it's just that your question
has no meaning. That's the straight and simple answer.

Y.Porat

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Jan 18, 2007, 12:14:32 PM1/18/07

to

Andy Resnick wrote:
> RolandRB wrote:
>
> > Let's say for just the sodium yellow line. What would the width of a
> > single photon and what is its length?
>
> A single photon of definite energy E = hv exists at zero spectral width,
> and infinite spatial and temporal extent.

-----------------------------
zero spacial width
and **infinit** (infinit' !!!!!) spacial temporal extent'''

is only in your fucken mathematics
just showing what realy you know about the real physical phenomemon

--------------------------------------------

>
> Coherent collections of photons, which together have a finite spectral
> width and originate from a finite-sized source, exist in a finite
> temporal pulse over a finite spatial extent.

--------------
and that sonds a bit better
but you still ddint answer the Op question

ATB
Y.Porat
---------------------------------

Igor

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Jan 18, 2007, 3:28:26 PM1/18/07

to

The width of a photon can be equated with its uncertainty in position,
which under minimal conditions is inversely proportional to its
uncertainty in momentum, as dictated by the Heisenberg Uncertainty
Principle.

Sam Wormley

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Jan 18, 2007, 5:18:29 PM1/18/07

to

The problem is your question.

Timo A. Nieminen

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Jan 18, 2007, 5:36:57 PM1/18/07

to

The straight and simple answer is zero and zero.

The photon is a quantum object. There is a wavefunction that tells you
where you might detect the photon; this wavefunction has a width and a
length (for a monochromatic plane wave, both are infinite). Then there is
the thing that you detect, the exchange of energy between the EM field and
matter, which appears to happen at a single point. Thus, a photon appears
to be of zero size. Compare with an electron, which also has a
wavefunction that can be of various widths and lengths, but when we look
for it appears to be at a single point.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

PD

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Jan 18, 2007, 10:27:28 PM1/18/07

to

I don't think it is a straight and simple answer, no. And there's
actually a bunch of interesting quantum mechanics that's involved in
explaining why it's not so simple. The first thing you need to disavow
is the preconception that fundamentally, particles are little things
with a center at a particular location and a definite size and shape.
It turns out that, fundamentally, things are not that at all. What they
are is much, much stranger.

Part of the problem is that there are at least two definitions of
photons:
1) a quantum state of the electromagnetic field with definite momentum
and energy and frequency, where the three are related by E = h*f = p*c.
2) the blob of light that gets detected in a photon detector and which,
by its detection, exhibits a definite location and therefore a
less-than-definite momentum.

The uncertainty principle says that you cannot have both. And in fact,
calculations that you would do to accurately predict the behavior of
photons would demand using a wavefunction that in principle spreads
over all space, even though you *know* that at the moment of detection
this wavefunction will have to "collapse" to some particular place.
There simply is no way to come up with a model of a little thing with
width and length that allows you to match up both of these
observations.

This peculiarity, this fuzziness, is not unique to photons. It is true
for everything from electrons to basketballs. It's just that at
conventional scales, we don't notice the fuzziness at all.

PD

Y.Porat

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Jan 19, 2007, 4:16:56 AM1/19/07

to

-----------------------
and if you follow this thread from top to bottom
it only shows us how little we really know
about real physics entities!!

may be lead to some more modesty of physicist who pretend to claim
that
'everything is under control
and how 'magnificent' is for instance QM
and all the mathematics around it
PS
this ignorance is just **the tip of the iceberg ** of

the** much wider ** unadmitted ignorance of people who consider
**themselves**
experts of physics .!!

ATB
Y.Porat
----------------------

ATB
Y.Porat
---------------------

Eric Gisse

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Jan 19, 2007, 4:19:02 AM1/19/07

to

Read about quantum mechanics and you will learn about how fundamental
the uncertainty principle is.

Or keep blathering incoherently about how much you don't understand or
like physics.

I think we both know which option you will follow.

WaveMechanic

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Jan 19, 2007, 7:08:03 AM1/19/07

to

"PD" <TheDrap...@gmail.com> wrote in message news:1169177248.2...@s34g2000cwa.googlegroups.com...

>
>
> On Jan 18, 6:05 am, "RolandRB" <rolandbe...@hotmail.com> wrote:
>> Let's say for just the sodium yellow line. What would the width of a
>> single photon and what is its length?
>>
>> I've tried doing a search and the amount of waffle is staggering. There
>> must be a straight and simple answer to this. Surely, somebody knows.
>
> I don't think

We know that, why do continue to tell everyone that you don't think?

> it is a straight and simple answer, no. And there's
> actually a bunch of interesting quantum mechanics that's involved in
> explaining why it's not so simple. The first thing you need to disavow
> is the preconception that fundamentally, particles are little things
> with a center at a particular location and a definite size and shape.
> It turns out that, fundamentally, things are not that at all.

Two"fundamentally's" in adjacent sentences. You don't think, do you?

> What they
> are is much, much stranger.

Definitely much much.

> Part of the problem is that there are at least two definitions of
> photons:
> 1) a quantum state of the electromagnetic field with definite momentum
> and energy and frequency, where the three are related by E = h*f = p*c.
> 2) the blob of light that gets detected in a photon detector and which,
> by its detection, exhibits a definite location and therefore a
> less-than-definite momentum.
>
> The uncertainty principle

You are definitely drooling off topic now.
He wants answers in units of length.

Quantum Ranger

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Jan 19, 2007, 9:09:57 PM1/19/07

to

It's not the length/width of a Photon that is to be questioned (a
photon has a simple energy value), it's the location one can detect it
that is tricky.

Y.Porat

unread,

Jan 20, 2007, 10:40:20 AM1/20/07

to

Quantum Ranger wrote:
> Y.Porat wrote:
> > PD wrote:
> > > On Jan 18, 6:05 am, "RolandRB" <rolandbe...@hotmail.com> wrote:
> > > > Let's say for just the sodium yellow line. What would the width of a
> > > > single photon and what is its length?
> > > >

> > > and shape.
> > > It turns out that, fundamentally, things are not that at all. What they
> > > are is much, much stranger.
> > >
> > > Part of the problem is that there are at least two definitions of
> > > photons:
> > > 1) a quantum state of the electromagnetic field with definite momentum
> > > and energy and frequency, where the three are related by E = h*f = p*c.
> > > 2) the blob of light that gets detected in a photon detector and which,
> > > by its detection, exhibits a definite location and therefore a
> > > less-than-definite momentum.
> > >
> > > > >

----------------------
'tricky' is just another word for
'we dont know a fuck about it- in less polite
and pompous words!!

(it is only the little fucker student from Alaska that knowes everthing
except ther fact that he is a small pomous rediculous kuku

Y.Porat
-------------------------

Eric Gisse

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Jan 20, 2007, 8:02:08 PM1/20/07

to

No, he used "tricky" because he didn't feel like explaining the
uncertainty principle to you.

>
> (it is only the little fucker student from Alaska that knowes everthing
> except ther fact that he is a small pomous rediculous kuku

I have a more substantial background in physics than you do, you senile
old bat.

>
> Y.Porat
> -------------------------

Y.Porat

unread,

Jan 21, 2007, 2:58:35 AM1/21/07

to

Eric Gisse wrote:
> Y.Porat wrote:
> > Quantum Ranger wrote:
> > > Y.Porat wrote:
> > > > PD wrote:
> > > > > On Jan 18, 6:05 am, "RolandRB" <rolandbe...@hotmail.com> wrote:
> > > > > > Let's say for just the sodium yellow line. What would the width of a
> > > > > > single photon and what is its length?
> > > > > >
> >

---------------------
fucken disturbed undergraduated moron Napoleon Bonaparte Shaise Eric
go discuss and fuck youself with your fucken nazi shit father!!
not with me

Y.Porat
-----------------------------

Eric Gisse

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Jan 21, 2007, 4:41:48 AM1/21/07

to

Doesn't it absolutely suck that I know more about physics than you do?

>
> Y.Porat
> -----------------------------

Y.Porat

unread,

Jan 21, 2007, 10:41:01 AM1/21/07

to

Eric Gisse wrote:
> Y.Porat wrote:
> > Eric Gisse wrote:
> > > Y.Porat wrote:
> > > > Quantum Ranger wrote:
> > > > > Y.Porat wrote:

> > > > > > > about real physics entities!!

> > > > > > > > ATB
> > > > > > Y.Porat
> > > > > > ---------------------
> > > > >
> > > > > It's not the length/width of a Photon that is to be questioned (a
> > > > > photon has a simple energy value), it's the location one can detect it
> > > > > that is tricky.
> > > > ----------------------
> > > > 'tricky' is just another word for
> > > > 'we dont know a fuck about it- in less polite
> > > > and pompous words!!
> > >
> > > No, he used "tricky" because he didn't feel like explaining the
> > > uncertainty principle to you.
> > >
> > > >
> > > > (it is only the little fucker student from Alaska that knowes everthing
> > > > except ther fact that he is a small pomous rediculous kuku
> > >
> > > I have a more substantial background in physics than you do, you senile
> > > old bat.
> > ---------------------
> > fucken disturbed undergraduated moron Napoleon Bonaparte Shaise Eric
> > go discuss and fuck youself with your fucken nazi shit father!!
> > not with me
>
> Doesn't it absolutely suck that I know more about physics than you do?
>

> > -----------------------------

(:-)
Hi little undergarduated disturbed Napoleon Bonaparte
go see a psychiatrist soon

Y.Porat
---------------------------------------

s...@microtec.net

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Jan 21, 2007, 11:46:06 AM1/21/07

to sr...@globetrotter.net

RolandRB a écrit :

Presently, there has to be straight and simple answers to all
fundamental
issues, but nobody really knows yet about this one.

Since the advent of the Copenhagen interpretation of Quantum Mechanics
underlied by Heisenberg's uncertainty principle, all further research
into further
clarifying this issue has been abandonned as being impossible.

For a while some prominent physicists tried to counter the trend, like
Einstein, de Broglie, Planck, Bohm, and many others, but they could
not reverse the trend and cause research to resume.

They were called causalists.

Maybe some day common sense will prevail again and research
resume.

In the mean time, everybody is on his own on this and many other
unresolved issues.

André Michaud

Eric Gisse

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Jan 21, 2007, 3:49:24 PM1/21/07

to

Stop crying, Porat. Your psychosis bores me.

>
> Y.Porat
> ---------------------------------------

Y.Porat

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Jan 22, 2007, 11:21:00 AM1/22/07

to

-----------------------------------
go fuck youself with your Nazi shit father !!
and add your Nazi shit mother
as well
and go see your psychiatrist as well
(anyway it will not help!!)
Y.P
------------

Eric Gisse

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Jan 22, 2007, 12:10:17 PM1/22/07

to

Stop crying, Porat.

> Y.P
> ------------

Y.Porat

unread,

Jan 23, 2007, 4:50:31 AM1/23/07

to

Eric Gisse wrote:
> Y.Porat wrote:
> > Eric Gisse wrote:
> > > Y.Porat wrote:
> > Photon that is to be questioned (a
> >
> > > > >

> > > go fuck youself with your Nazi shit father !!
> > and add your Nazi shit mother
> > as well
> > and go see your psychiatrist as well
> > (anyway it will not help!!)
>
> Stop crying, Porat.

------------------------
go fuck youself with yourfucken mother
that raised a sub human like you
and discuss with her not with me !!

Y.P
---------------------------------
>

Eric Gisse

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Jan 23, 2007, 6:03:05 AM1/23/07

to

Y.Porat wrote:
> Eric Gisse wrote:
> > Y.Porat wrote:
> > > Eric Gisse wrote:
> > > > Y.Porat wrote:
> > > Photon that is to be questioned (a
> > >
> > > > > >
> > > > go fuck youself with your Nazi shit father !!
> > > and add your Nazi shit mother
> > > as well
> > > and go see your psychiatrist as well
> > > (anyway it will not help!!)
> >
> > Stop crying, Porat.
> ------------------------
> go fuck youself with yourfucken mother
> that raised a sub human like you
> and discuss with her not with me !!

This is what I imagine you look like after reading one of my posts:

http://www.bbc.co.uk/parenting/images/300/baby_crying_closeup.jpg

>
> Y.P
> ---------------------------------
> >

Y.Porat

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Jan 23, 2007, 6:29:37 AM1/23/07

to

> > ---------------------------------
go fuck yourself with your Nazi shit mother
and discuss with her
you can add to it your Nazi shit father as well

you have nothing to discuss with me

> > Y.P
> > ---------------------------------
> > >

G=EMC^2 Glazier

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Jan 23, 2007, 8:57:18 AM1/23/07

to

Porat 6 trillion photons can sit side by side on the point of a pin.
That means if you know the diameter of the pin head divide it by 6
trillion,and it will give you the size of one photon go figure
Bert.

hanson

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Jan 23, 2007, 11:12:56 AM1/23/07

to

Herbie Shmerbie "G=EMC^2 Glazier" <herbert...@webtv.net>
the great PHOTON FIGURER figured in message to Yehi Porat:
news:26611-45B...@storefull-3338.bay.webtv.net...

[hanson]
Before you tell Yehi to "go figure"... ahahaha... tell us how you
"figured" to count these 6 trillion photons? Then tell us you how
you "figured" the width your *point*...
Thanks for the laughs, I "figure"... ahahaha... ahahahanson

MathMagician

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Jan 23, 2007, 12:26:27 PM1/23/07

to

"hanson" <han...@quick.net> wrote in message news:cuqth.530$FN1.189@trnddc08...

I like to go figure...
A photon is this "big":
http://www.androcles01.pwp.blueyonder.co.uk/photonsphere.gif

Blue surface - Negative charge
Red - Positive
Gold - North
Purple - South

The slower it operates, the bigger it is, it has more time to expand.

Some photons are so fast we call them "protons".
Other photons are just fast enough to be called "electrons".
That's why energy and mass are equivalent, E = mc^2 = h(nu).
I have grave doubts about the Bohr "solar system" atom as a
model.
The big question is how the electron manages to have its outside
always "blue" and the smaller and "heavier" proton always "red"
with gravity playing the part of the other pole.

exp(i.t) = -1 for t = 0, 2pi, 4pi, 6pi ... 2n.pi, the other pole
is (0,i0)
http://www.androcles01.pwp.blueyonder.co.uk/Euler.xls

hanson

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Jan 23, 2007, 1:03:19 PM1/23/07

to

Portrayed here is an entirely new way of how to look at
the nature of the electric charge, by Andro, the
"MathMagician" <Ma...@Magic1.co.uk> wrote in message
news:7zrth.151570$Kh7....@fe2.news.blueyonder.co.uk...

>
"hanson" <han...@quick.net> wrote in message

news:cuqth.530$FN1.189@trnddc08... [snipped]
>
[Andro]

A photon is this "big":
http://www.androcles01.pwp.blueyonder.co.uk/photonsphere.gif

Blue surface - Negative charge
Red - Positive
Gold - North
Purple - South

The slower it operates, the bigger it is, it has more time to expand.

Some photons are so fast we call them "protons".
Other photons are just fast enough to be called "electrons".
That's why energy and mass are equivalent, E = mc^2 = h(nu).
I have grave doubts about the Bohr "solar system" atom as a
model.
The big question is how the electron manages to have its outside
always "blue" and the smaller and "heavier" proton always "red"
with gravity playing the part of the other pole.

exp(i.t) = -1 for t = 0, 2pi, 4pi, 6pi ... 2n.pi, the other pole
is (0,i0)
http://www.androcles01.pwp.blueyonder.co.uk/Euler.xls
>
>

[hanson]
You portray here an entirely new aspect/way to explain/describe
the nature of the electric charge. VERY INTERESTING!
BTW, what do the bottom figures, the summed/ex/diff values
mean? Note the peculiar size of your n^/n! diff ~ 2pi*E-10
when compared with the c ratios of resistivity or permittivity
of free space.
Good show, Andro. Excellent!
Thanks, Andro

Sam Wormley

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Jan 23, 2007, 2:19:39 PM1/23/07

to

Don't eat any yellow photons Herb.

Eric Gisse

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Jan 23, 2007, 3:04:24 PM1/23/07

to

Of course I don't.

You know nothing about physics.

>
> > > Y.P
> > > ---------------------------------
> > > >

Dumbledore

unread,

Jan 24, 2007, 12:11:55 PM1/24/07

to

"hanson" <han...@quick.net> wrote in message news:H5sth.541$FN1.7@trnddc08...

In the complex plane "real" numbers occupy the x-axis and
"imaginary" numbers occupy the y-axis. "Real" and "imaginary"
are terms that mathematicians use, but of course there is nothing
"real" or "imaginary" about a number; it has no mass, length or
time, no physical existence. A number is an idea and so "imaginary"
numbers are just as "real" as real numbers, we apply no special
significance to the terms except to say they are at right angles to
each other.
Any given point on the complex plane can be expressed in
cartesian (named for Rene Descartes, "I think, therefore I am")
coordinates in the form (x,y) or in polar coordinates (r, theta).

http://www.androcles01.pwp.blueyonder.co.uk/ComplexPlane.GIF

Thus the red point is both (4, pi/8) ((r, theta) or polar) and
(2.8284, i.2.8284) ((x,ix) or cartesian).
Multiplying an x value by i is a rotation in the complex plane,
so if we increase the angle to pi/4 (90 degrees) we move the red point
to (0,i4)(c) = (4, pi/2)(p).
Rotating still further to pi (180 degrees), we arrive at (-4, i0)(c) = (4, pi)(p)
and of course if we keep going we eventually arrive at (4, 2pi)(p) = (4,i0)(c)

Now...
I said above that multiplying by i was a rotation in the complex plane,
so if we multiply (0,4i) by i and arrive at (-4,0), then we also would have
(0, i1) * i = (-1,0).
Thus i * i = -1 and i is the sqrt(-1).
To write this correctly, I should say
(0,i)^2 =
(0, i) * (0, i) = 0^2 + 2( 0*i) + i^2
= (-1,0).

Now we come to Taylor's series (or really, McClaurin's series, Taylor
went a step further than McClaurin and he was an American, the
real work was done by McClaurin and we don't need Taylor's add on).

Without going into how the series was derived (I'm not sure I could
anyway, although I did know once -- man, I'm getting old) you'll see
that the terms of the series are interlaced to produce e^x with the
operator '+', and the sine and cosine series are the odd and even
terms with the operator i.
I hope I've shown that in the Euler.xls.

As to the final summation...
The exp(x) function gives the same result as the summation of the terms.
The cos(x) function gives the same result as the summation.
The sin(x) function gives the same result as the summation.

None should be surprising, since a program such as Excel
or pocket calculator uses a hidden library subroutine that does
the same calculation, computers can only add binary numbers
anyway.

The difference is simply that I did not use enough terms,
so I showed the difference.

This is what makes mathematics so fascinating and why Einstein's
garbage is such a disgusting load of tripe, holding back any real
investigation into how Nature really works. Math is PURE,
people are dogs only interested in making a name for themselves.
Mathematicians are not famous except to other mathematicians
and do not actively seek glory.

All-in-all mathematicians are really a humble lot, more interested in
their musings than Nature or mankind's rantings. Newton was a
mathematician, Einstein was not. Those that think Einstein was are
fools, for Einstein broke the strict rules of mathematics with his
pathetic appeals to "assume" 2AB/(t'A-tA) = c and his entire
house of cards is built on that. All the debate you see in the
newsgroups can be traced back to that single ridiculous assumption.

I'm an odd man out, I want to know about NATURE and I get
frustrated and angry with fuckwits... not a useful social trait.
Herbie doesn't trouble me, he's a halfwit and the same goes for
a lot of the others. It's the real fuckwits like Roberts and Steve
Lawrence (sal) and Baez and Carlip and Edward Green and Timo
whatever-his-name-is that piss me off. They think they are God's gift
to physics and they are all FUCKIN' USELESS, adding confusion
to the pot. The sad thing is they are just intelligent enough to be
coherent and just stupid enough to be dogmatic and argumentative.

We can dismiss the Peters Brown (Pmb), the Dorks Van de merde
(D Vdm) and the Phuckwits Duck (PD), they do not trust even
themselves to write their own names they are so illiterate.

I don't know what mass is. All I do know is that we measure it
using force.
I don't know what charge is. All I do know is that we measure it
using force.
I don't know what marge (the magnetic equivalent of charge and mass)
is. All I do know is that nobody measures it at all, it didn't even have
a name until I gave it one.
Say "magnetic monopole" and they'll all have a conniption, it's not in
their text books.
Marge is the missing link, the next step in the puzzle. It provides
the missing third dimension, a point *above* the complex plane
to give us a complex volume with the force field axes Electric,
Magnetic and Gravity, the GEM model of the universe. Instead
of pondering what action-at-a-distance is, we *start* with the
action-at-a-distance and ponder what matter is.

What I'm trying to say is that like the point (4, pi/8) is the same point
as (2.8284, i.2.8284), merely described differently, an atom is the same
animal whether it is a Bohr atom or a GEM atom, we rely on the
natural numbers for our description of the elements and their isotopes,
as in Hydrogen 1 ... Carbon 12,14 ... Uranium 235, 238.

A different description should lead to new insights. For example,
the nucleus of a Bohr atom is made of protons and neutrons with
an electron cloud surrounding it, but a GEM atom has only forces
and frequencies.

The language of physics is mathematics, but mathematics has
very strict rules which if broken will lead to nonsense.

There is more I do not know than I ever will, I must remain
content that I have discovered planets nobody will see.
I will die in that knowledge, I was the only one it mattered to anyway.
http://www.androcles01.pwp.blueyonder.co.uk/Algol/Algol.htm
http://www.androcles01.pwp.blueyonder.co.uk/Wendy/Wendy.htm

Like my lion, Newton, I stand upon the shoulders of giants and have
seen further than any man before me.
I do not crawl beneath the knees of pygmies like Einstein.

Your humble servant,
Androcles, Sorcerer and Mathmagician.
http://www.androcles01.pwp.blueyonder.co.uk/
HAHahahaha..aha...aha..ha . . . h . . . . groan, sigh...

Dumbledore

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Jan 24, 2007, 12:12:48 PM1/24/07

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"hanson" <han...@quick.net> wrote in message news:H5sth.541$FN1.7@trnddc08...

In the complex plane "real" numbers occupy the x-axis and

"imaginary" numbers occupy the y-axis. "Real" and "imaginary"
are terms that mathematicians use, but of course there is nothing
"real" or "imaginary" about a number; it has no mass, length or
time, no physical existence. A number is an idea and so "imaginary"
numbers are just as "real" as real numbers, we apply no special
significance to the terms except to say they are at right angles to
each other.
Any given point on the complex plane can be expressed in
cartesian (named for Rene Descartes, "I think, therefore I am")
coordinates in the form (x,y) or in polar coordinates (r, theta).

http://www.androcles01.pwp.blueyonder.co.uk/ComplexPlane.GIF

Thus the red point is both (4, pi/8) ((r, theta) or polar) and

[2.8284, i.2.8284] ([x,ix] or cartesian).

I've deliberately chosen square brackets for cartesian coordinates
and parentheses for polar, it has nor special significance except
for this tutorial.

Multiplying an x value by i is a rotation in the complex plane,
so if we increase the angle to pi/4 (90 degrees) we move the red point

to [0,i4] = (4, pi/2).
Rotating still further to pi (180 degrees), we arrive at [-4, i0] = (4, pi)
and of course if we keep going we eventually arrive at [4,i0] =(4, 2pi).

Now...
I said above that multiplying by i was a rotation in the complex plane,

so if we multiply [0,4i] by i and arrive at [-4,0], then we also would have
[0, i1] * i = [-1,0].

To write this correctly, I should say

[0,i]^2 =
[0, i] * [0, i] = 0^2 + 2[0*i] + i^2
= [-1,0]

A rotation of pi (180 degrees) in the complex plane is
a multiplication by -1.

Thus i * i = -1 and i is sqrt(-1).

Now we see that 4 has two square roots, 2 and -2,
it has 4 fourth roots, 2,2i,-2,-i2 and...
tada!
It has three cube roots!
(2, 2pi/3)
(2,4pi/3)
(2,0)

At this stage one usually sets the student some homework
and says "show (2, 2pi/3)*(2, 2pi/3)*(2, 2pi/3) = [4,i0] using
cartesian coordinates" and that is where Gisse would say
"I don't give a shit about proof", and where he loses the
most valuable thing he could gain from it, insight.

Now we come to Taylor's series (or really, McClaurin's series, Taylor
went a step further than McClaurin and he was an American, the

real work was done by McClaurin).

Without going into how the series was derived (I'm not sure I could
anyway, although I did know once -- man, I'm getting old) you'll see
that the terms of the series are interlaced to produce e^x with the
operator '+', and the sine and cosine series are the odd and even
terms with the operator i. I hope I've shown that in the Euler.xls

spreadsheet.

As to the final summation...
The exp(x) function gives the same result as the summation of

the terms above,
the cos(x) function gives the same result as the summation,
the sin(x) function gives the same result as the summation,
thus proving Taylor and McClaurin were correct.

This should not be surprising, since a program such as Excel

or pocket calculator uses a hidden library subroutine that does

the same calculation computers can only add binary numbers
anyway.

The difference is simply that I did not use enough terms,

so I showed the (very small) difference.

This is what makes mathematics so fascinating and why Einstein's
garbage is such a disgusting load of tripe, holding back any real

scientific investigation into how Nature works. Math is PURE,

people are dogs only interested in making a name for themselves.

Einstein was definitely a dog who maliciously misused mathematics
for his own personal gain. Hence his quote about his castles in the air
you've used on occasion.
I cannot believe he was so stupid as to not know what he was about,
therefore he set out to deliberately deceive as any stage magician
does. The only difference is the public knows the stage magician
is an entertainer. Einstein was more in the class of the fortune-teller,
the Uri Geller spoon bender, the charlatan. It's all sleight-of-hand,
smoke and mirrors, and Einstein performed his trick on paper.
As members of the audience it is our job to figure out how the magic
trick was done, not argue whether it is real or not.
That I've done, its all on my web page.

Mathematicians are not famous except to other mathematicians

and do not actively seek glory. Occasionally the paperazzi will
seek them out, but the mathematician simply cannot be bothered
by such shinnagans. That's why I prefer to hide behind a pseudonym.

All-in-all mathematicians are really a humble lot, more interested in
their musings than Nature or mankind's rantings. Newton was a
mathematician, Einstein was not. Those that think Einstein was are
fools, for Einstein broke the strict rules of mathematics with his
pathetic appeals to "assume" 2AB/(t'A-tA) = c and his entire
house of cards is built on that. All the debate you see in the
newsgroups can be traced back to that single ridiculous assumption

that any real mathematician would laugh at.

I'm an odd man out, I want to know about NATURE and I get
frustrated and angry with fuckwits... not a useful social trait.
Herbie doesn't trouble me, he's a halfwit and the same goes for

a lot of the others. It's the real fuckwits like Roberts and Lawrence

(sal) and Baez and Carlip and Edward Green and Timo
whatever-his-name-is that piss me off.
They think they are God's gift to physics and they are all FUCKIN'

USELESS, adding only confusion to the pot. The sad thing is they

are just intelligent enough to be coherent and just stupid enough to
be dogmatic and argumentative.

We can dismiss the Peters Brown (Pmb), the Dorks Van de merde
(D Vdm) and the Phuckwits Duck (PD), they do not trust even

themselves to write their own names, they are so illiterate.

I don't know what mass is. All I do know is that we measure it

using force. We stand on the bathroom scale and take a reading.

I don't know what charge is. All I do know is that we measure it
using force.
I don't know what marge (the magnetic equivalent of charge and mass)
is. All I do know is that nobody measures it at all, it didn't even have
a name until I gave it one.
Say "magnetic monopole" and they'll all have a conniption, it's not in
their text books.
Marge is the missing link, the next step in the puzzle. It provides
the missing third dimension, a point *above* the complex plane
to give us a complex volume with the force field axes Electric,
Magnetic and Gravity, the GEM model of the universe. Instead
of pondering what action-at-a-distance is, we *start* with the
action-at-a-distance and ponder what matter is.

What I'm trying to say is that like the point (4, pi/8) is the same point

as [2.8284, i.2.8284],
http://www.androcles01.pwp.blueyonder.co.uk/ComplexPlane.GIF
merely described differently; an atom is the same animal whether it is

a Bohr atom or a GEM atom, we rely on the natural numbers for our
description of the elements and their isotopes,
as in Hydrogen 1 ... Carbon 12,14 ... Uranium 235, 238.

A different description should lead to new insights. For example,
the nucleus of a Bohr atom is made of protons and neutrons with
an electron cloud surrounding it, but a GEM atom has only forces
and frequencies.

The language of physics is mathematics, but mathematics has
very strict rules which if broken will lead to nonsense.

There is more I do not know than I ever will, I must remain
content that I have discovered planets nobody will see.
I will die in that knowledge, I was the only one it mattered to anyway.
http://www.androcles01.pwp.blueyonder.co.uk/Algol/Algol.htm
http://www.androcles01.pwp.blueyonder.co.uk/Wendy/Wendy.htm

Like my lion, Newton, I stand upon the shoulders of giants and have
seen further than any man before me.
I do not crawl beneath the knees of pygmies like Einstein.

1) Frustra fit per plura, quod fieri potest per pauciora.
It is vain to do with more what can be done with less.

-- William of Ockham circa 1288 - 1348

2) We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. -- Sir Isaac Newton, 1643 - 1727

3) Everything should be as psychotic as possible, but not simpler. --Albert Einstein 1879 - 1955

4) "But the ray moves relatively to the initial point of k, when measured in the stationary system, with the velocity c-v" --Albert Einstein 1879 - 1955

5) "It follows, further, that the velocity of light c cannot be altered by composition with a velocity less than that of light." --Albert Einstein 1879 - 1955

3) is derived from 4) and 5).

Dumbledore

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Jan 24, 2007, 12:13:07 PM1/24/07

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"hanson" <han...@quick.net> wrote in message news:H5sth.541$FN1.7@trnddc08...

In the complex plane "real" numbers occupy the x-axis and

Dirk Van de moortel

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Jan 24, 2007, 12:49:52 PM1/24/07

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"Dumbledore" <Headm...@hogwarts.physics_n> wrote in message news:ksMth.134708$QY6....@fe1.news.blueyonder.co.uk...

[snip website copy]

> Your humble servant,
> Androcles, Sorcerer and Mathmagician.

Dirk Vdm

Dumbledore

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Jan 24, 2007, 1:21:25 PM1/24/07

to

"Dirk Van de moortel" aka
"Dork Van de merde"
"Dork Van de psychopath"
"Dork Van de psychotic fumble mumbler"
"Dork Van de fuckhead" <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote in message news:4%Mth.307710$DA5.6...@phobos.telenet-ops.be...
[anip]

http://users.telenet.be/vdmoortel/dirk/Physics/TwinsEvents.html
"We use 3 inertial reference frames" [because Dorks can't get the result
they want in two].
"In neither of these frames any form of acceleration is felt" [neither one of
all three].
"In order for the travelling twin to make HIS trip, SHE must be in frame S'
while going away".
"if T = 5 years and v = 0.8c, then the stay at home twin will have aged
10 years".

Belgium is where the farts blow.

"Your conclusion is dead wrong.
Start over, but skip the first part and the conclusion." -- Dork Van de
fuckhead.

"You made a mistake" -- Dork Van de psychotic fumble mumbler.

ASSistant professor Paul B. Andersen, tusseladd:

"That is, we can reverse the directions of the frames
which is the same as interchanging the frames,
which - as I have told you a LOT of times,
OBVIOUSLY will lead to the transform:
t = (tau-xi*v/c^2)/sqrt(1-v^2/c^2)
x = (xi - v*tau)/sqrt(1-v^2/c^2)
or:
tau = (t+xv/c^2)/sqrt(1-v^2/c^2)
xi = (x + vt)/sqrt(1-v^2/c^2)"