Re: Understanding SR - simultaneity

Spoonfed wrote:
I snipped off the beginning and end for brevity.


Sue... wrote:
Spoonfed wrote:
Well, does light depend on the acceleration of an electron or proton?


Short answer--both. The proton and electron should both have an equal
change in momentum perpendicular to the path of the photon; two
momentum changes, two events. Two simultaneous events generate the
photon, and two simultaneous events absorb the photon.

That seems reasonable but you might consult a QED text and
how a Feynman diagram is discussed for that interaction.
I just call it a standing wave.



The farther we are from the electron, the less Coulomb force/coupling
we have to get it moving.

Beyond a short distance, the electron won't be in the atom to fall into
a lower orbital shell. But antennas, transmitters, etc. generate
photons too.

No they do not. They use the motion of loosely bound electrons.
You won't detect any copper line spectra in the emissons of your
favorite radio station tho' the coupling structure is likely copper.


And these photons are not emitted by falling through
atomic quantum levels. But they ARE quantum levels, just the same...
just not atomic.

No dice.
http://www.eso.org/projects/vlti/


Tie 3 meters of elestic cord to a roller
skate.
Displace the free end 1 meter and measure the time lag for the skate to
move 1 meter.
Stack the other skake (assuming you have two feet)
to double the weight and repeat.
That looks like a good mechanism
for retarded potential to me.
Somewhere down the skating rink we'll
want to remember that Coulomb force and spring tension have an
inverse relationship regarding the end to end distance. Forgetting
that makes magnetism and permeability look whacked.


I am not getting the image or the analogy here.
http://hyperphysics.phy-astr.gsu.edu/Hbase/waves/string.html
http://physics.nist.gov/cuu/Images/alphaeq.gif
http://physics.nist.gov/cuu/Constants/alpha.html


Your Feynman article gets very close to the issue I'm getting at, but
seems to veer off. Here is what Feynman says:

"...I learned what was wrong with the idea that an electron does not
act on itself. When you accelerate an electron it radiates energy and
you have to do extra work to account for that energy. The extra force
against which this work is done is called the force of radiation
resistance. The origin of this extra force was identified in those
days, following Lorentz, as the action of the electron itself."

Now, another detail lies in an undergraduate text book that I have in
my possession. Modern Physics (Bernstein, Fishbane, Gasiorowicz)
Example 3-8.
"From the point of view of quantum mechanics, light is carried by
photons, symobolyzed, gamma. According to the quantum mechanical rules
of electricity and magnetism, a photon can be absorbed by a charged
particle such as an electron. Show, by applying the laws of
conservation of energy and momentum, that a truly free electron cannot
absorb a photon; that is, show that the process gamma + e --> e is not
possible."

Before reading this, I had long though it very strange that electrons
running in loops (thus undergoing constant acceleration) generate no
photons, and yet photons are so often described as being caused by
accelerating charges. But this example showed quite easily that an
accelerating charge cannot by itself create a photon without violating
conservation laws.

No argument from me.

Right, once again--you need both charged particles to create a photon.
And not only that, I think you need a quantum change in momentum state
I don't ?recall? infering photons could be created. They are emitted
and
absorbed. They have to wear wrist watches, but have no arms, they have
to explore all paths, but have no legs, they have to carry a magnetic
monopole but magnetic monopoles do not exist.
http://www.physics.yorku.ca/undergrad_programme/highsch/Feynm4.html
{good thing you snipped some space above}

<<Now, does not the prize to Einstein imply
that the Academy recognised the particle
nature of light? The Nobel Committee says
that Einstein had found that the energy exchange
between matter and ether occurs by atoms emitting
or absorbing a quantum of energy,hv .

As a consequence of the new concept of light quanta
(in modern terminology photons) Einstein proposed the
law that an electron emitted from a substance by
monochromatic light with the frequency has to have
a maximum energy of E=hv-p, where p is the energy needed to
remove the electron from the substance. Robert Andrews
Millikan carried out a series of measurements over a
period of 10 years, finally confirming the validity of this
law in 1916 with great accuracy. Millikan had, however,
found the idea of light quanta to be unfamiliar and strange.

The Nobel Committee avoids committing itself to the
particle concept. Light-quanta or with modern terminology,
photons, were explicitly mentioned in the reports on
which the prize decision rested only in connection with
emission and absorption processes. The Committee says
that the most important application of Einstein's photoelectric
law and also its most convincing confirmation has come from
the use Bohr made of it in his theory of atoms, which explains
a vast amount of spectroscopic data. >>
http://nobelprize.org/physics/articles/ekspong/index.html


My interpretation of this has been to assume that a photon can only be
generated by the interaction of two charged particles. Feynmann seems
to have gone a different direction becaus he is still trying to answer
his question, continuing,

"The first term of this action, of the electron on itself, gave a kind
of inertia (not quite relativistically satisfactory). But that
inertia-like term was infinite for a point-charge. Yet the next term
in the sequence gave an energy loss rate, which for a point-charge
agrees exactly with the rate you get by calculating how much energy is
radiated."

Synchrotron radiation I presume.


...which I can't make any sense of at all, but he seems to come back to
reality, with...

"So the force of radiation resistance, which is absolutely necessary
for the conservation of energy would disappear if I said that a charge
could not act on itself."

I think he is describing the electron moving near the speed of
light wrt lots of neigboring positive charge urging it on.

Googling Synchrotron radiation, Smith Purcell radiation
Wiggler undulator will probably yield some clarity.


Then, in the following few paragraph, Feynman gets into the crux of the
small part of the issue that I feel I have a tentative grasp of.
Namely that the emission and absorption of a photon represents the
interaction of four particles--two at the emitting end, and two at the
aborption end. At the emitting end, an electron is dropping into a
lower available quantum energy level, while at the absorbing end, an
electron is popping out of an available quantum energy level.

For a four particle universe, that seems reasonable.


Two atoms. Four particles. One pair sends the radiation. The other
pair receives. Sometimes it's not two atoms--it's anywhere where
quantum momentum states can be established between pairs of particles.
....with some predictible degree of certainty? Causality? Probability?

Fundamental assumption of QM are easy to forget when you
interpret classically but that's no excuse for magic.

The radiation was alway there. No pairs have to send anything.
Stretch a bungee cord from Giza to the Eiffel tower, Then release
it. It does not have to wait for approval from Egypt to begin moving
away from you. It is instant. A strain gauge in Egypt won't indicate
that you have released the cord for some period time. A function
of the cord's mass and tension.

The Coulomb gauge is sometimes called the radiation gauge.
http://arxiv.org/abs/physics/0204034




Now, the spacetime interval between the emission and absorption
sqrt(c^2*t^2 - x^2) is zero, thus neither spacelike nor timelike. But
there are also two events at each end of the photon--the acceleration
of the source charges toward one another, and the acceleration of the
absorbing charges away from one another. These events should also have
some spacetime interval between them, which I would presume also
calculates to zero.

The ~charge~ of the intervening volume of space becomes
more positve or more negative. The absorber rotates CCW
or CW appropriately. I see one cause, one effect.

The absorber is a dipole...Two independent charges acting
simultaneously in reaction to one photon.

What makes them independent ? Coulomb's Law repealed ?
They can react to a photon. It doesn't exist 'till absorbed.
Before absorbtion the emisson of many photons may contribute
to the absorbed energy so it not ONE photon.




Instead of considering collisions, we also need to
consider closeness. A pair of hydrogen atoms and a
pair of helium atom may have a different idea about what
*close* means. So we represent fundamental charges as
a density (of pseudo particles) and use superposition to
determine what is *close*.

I think you've lost me.
Back up about three laps. I am right in the dust
you left me in. :o)


"Time-independent Maxwell equations"
http://farside.ph.utexas.edu/teaching/em/lectures/node26.html
http://en.wikipedia.org/wiki/Multiple_integral (shared volumes)

What is imaginary? The psuedo particles we represented
the electrical field with. They are integrable but not countable.

Bodies AND their associated fields share space with some
respect to time.

Well, okay. I hear some echoes of Tim's argument here. I'm not quite
clear on it, though.

The best online example I know is the triple integral to
derive magnetic force from coulomb force. It is just
a 3D superposition of moving water sprinklers. But
some of them squirt (+) and some of the suck (-).



We can't count the pseudo particles of our
own creation to see if they are *simultanieouly* in the same
place. They are only where we imagined them to be.


I would say this is all in agreement with some interpretation of
Quantum Mechanics.

I would say some of Quantum Mechanics is in agreement
with this. :o)

Hmmm I would hope we could agree
that a roof shouldn't look like a door and 2 windows and
the front of a house should not look like shingles.

QM and Classical fields are loosely speaking,
orthogonal views.



So we need a way to represent a degree
(the overlap of associated fields) of simultaniety
To do this we put space and time on and equal footing.
(Lorentz transform)

The interaction in the shared volumes of spaces is
evaluated with respect to their separation in space
or time.

What is imaginary? The equivalance of space and time.
Time-dependent Maxwell's equations (vector imaginaries)
http://farside.ph.utexas.edu/teaching/em/lectures/node41.html
http://www.wolfram-stanek.de/maxwell_equations.htm


You've probably handed me a perfectly good wheel, but I don't know
exactly what it is. I may try using it as a telephone while I
re-invent it. Anyway, I printed out wolfram-stanek. Maybe I'll glean
something.

Great! I forgot that included:
"Maxwell's equations considering quantum field theory"
which may speak more to you symbolically than I can
with a thousand water sprinklers.



The gradient of the Coulomb field, equated to the statistics
of a normal distribution is where a link between the
Hilbert space and Lorenz space ~can~ have validity.


Hilbert space is the coefficients of one of those Schrodinger
functions, right?
That is beyond me. Here is a more formal statement also
over my head:
<< In mathematics, a rigged Hilbert space (Gelfand triple,
nested Hilbert space, equipped Hilbert space) is a construction
designed to link the distribution (test function) and square-integrable

aspects of functional analysis. Such spaces were introduced to
study spectral theory in the broad sense. They can bring together
the 'bound state' (eigenvector) and 'continuous spectrum', in one
place. >>
http://en.wikipedia.org/wiki/Rigged_Hilbert_space


Ask me again a year from now. I'm going back to school for a math
degree, hoping to penetrate what I currently perceive as a maze of
infinitely self-referential and circularly defined mathematical jargon.

Indeed, you need both physics and a maths to sort it all out.
It HAS become a mess.


But you might consider this... If you have a box with a particle in
it, at all times that you are not detecting the particle, you know that
it is not actually hitting the sides of the box. During these times,
you can say that the probability of touching the sides is zero, and
anywhere else, you have no idea.

So you make up a *completely* arbitrary function. How do you determine
a completely arbitrary function? With a series representation with
unknown coefficients:

For instance Sum(A_n x^n, {n,0,infinity})

In fact, this is the only one you really need. Every other function,
Sin(x), Cosine(x), e^(x), Bessel Functions, Legendre Polynomials etc,
are representations of Sum(A_n x^n, {n,0,infinity}).

Once you know you have a particle trapped in a box, and set the chances
of it hitting the side as zero, representing it in the form of Sum(A_n
x^n, {n,0,infinity}) is going to look extremely messy, while
representing it in the form of Sum(B_n Sin(Pi*x/L*n)) will look very
classy, because it is immediately obvious that every term will evaluate
to zero at the two ends of the box.

How? I don't!

Oh, sorry, of course not. I'm writing like a textbook I get mad at.
Sorry. When x=0, you have Sin(0), and when x=L, you have Sin(n*Pi)
which is zero as long as n is an integer. So no matter how many terms
you have in it, it will always evaluate to zero at the ends.

Ya lost me. Or maybe your photons lost their watches and monopoles.
You can clarify or snip when you decide which.

There comes a point where the abstraction of
waves to particles to preserve an implausibe propagation model
I just use the classical field models and never contact that sort
of dice game. In the sub atomic realm, that is all you have to
work with so I am not discouraging your aspirations to higher
levels of abstration.


As you wish.


If I recall correctly, (and please don't take my word for it, because I
was taking several very hard classes and my thinking was quite muddled)
taking second derivatives of these functions with respect to position
will lead you to the momentum as a function of position. Also, IIRC,
these derivatives come out to real values if only one coefficient B_n
is nonzero, but they come out to be imaginary if more than one
coefficient B_n is nonzero. This momentum is associated with
particular wavelengths, and then all of the deBroglie wavelengths
coming out of the system turn out to be representable by single
coefficients instead of sums of several coefficients.

I'll have to take your word for it because I surely don't know.

After doing all this complex mathematical work, it is easy to forget
what is missing from the description is that this only describes the
particle when it is *not* hitting the edges of the box, and we also
have no idea as to when it last hit the edge of the box.

Your ~failure~ to classically superposition the four charges above
is probably a good example. You can probably drive an automobile
if you have never seen one from the outside. You'll drive it much
better if you have some image of wheels interacting with the road
surface.
http://farside.ph.utexas.edu/teaching/em/lectures/lectures.html :-)
http://web.mit.edu/8.02t/www/802TEAL3D/teal_tour.htm


I can't usually identify a wheel unless I am lucky enough to reinvent
it.
LOL

It seems to me that if we tried to describe the situation when the
particle *is* hitting the edge of the box we have a probability of
one-hundred percent at the collision point and zero everywhere else.
This might be related to the go/no-go test you were talking about as a
*go*, whereas the situation of not hitting the edge of the box
described by QM would be a *no-go*

Charges don't have edges like automobile bumpers.
So you integrate pseudo charges over space or you
integrate a probability amplitude. The go/no-go test
is an atomic oscillator. Either it absorbs or it does
not. Some particular oscillator may respond to
the light of the moon, only because a crack in
the door of your microwave oven provided the final
nudge. (bias lamp)


By the "classical" viewpoint, I think you are right. Charge is assumed
to be a perfect fluid, infinitely divisible. But the go/no-go test you
mention is an atomic oscillator, which is a quantum device. Use an
antenna as your go/no-go test instead

Perfect is in the eye of the beholder. Our discussion is cross
dicipline so
ethanol the perfect fluid so long as you don't waste it as a
motor fuel.

QM has enough warts you don't want to scale it up just to
apply a threshold detector over a broader domain. QED
strikes the best balance. You are sugesting a broader
application of statistics (just like a maths nut). Feynman
opted for more determinancy with his use of clocks and
monopoles. So all the mirrors that QM broke, started
working again when the clocks and monpoles restored
phase information.




Remembering the Heisinberg uncertainty principle, try
to identify what is determined by statistics and what is
processed as a probability amplitude.


Of course, remembering the HUP, (and reference to external measuring
devices or particles,) the accuracy of locating the exact position and
time of the *go* event is related to our uncertainty in the momentum
and energy of the event. Where, along the wavelength of a photon or
deBroglie wavelength of a particle, is it absorbed? When along one
oscillation of frequency is the photon (or deBroglie frequency of a
particle) absorbed? Does this information exist as an unmeasurable
quantity, or does it simply not exist? I've heard tell of a proof
suggesting that the information does not exist, but most of my
textbooks are at the undergraduate level, and consider this proof to be
beyond the scope.

AFAIK, no physical proof is necessary. It is mathematically
fundamental just like the inverse square law or pi or normal
distribution.


What you say is very strange. There are derivations to find Pi, normal
distributions, inverse square law--they may lead very clearly from
first principles, but they aren't first principles themselves--not that
you can't start with them as first principles, necessarily.

I also can't offer you proof a coin will come up heads 50% of
the time.

Look at some real world ~violations~. They really aren't, of course,
they are just loopholes in the formalism.

http://www.cco.caltech.edu/~qoptics/cqed.html






QED's sucesses in the subatomic realm exemplify
when a marriage of Lorenz and Hilbert space is on
sound footing.
http://nobelprize.org/physics/laureates/1965/feynman-lecture.html
The twins paradox exemplifies when it is not.


Goodness gracious, Miss Dominatrix, you make me read a lot.

Likewise. But you wern't suppose to read so much of Feynman's
war stories.

But I like them! I have similarities to Feynmann as an undergraduate
in that I am inspired "not by the parts in which everything [is] proved
and demonstrated carefully and calculated, because I [can't] understand
those very well," Unfortunately, I never developed his attitude as an
undergraduate in Electrical Engineering that "since they didn't get a
satisfactory answer to the problem I wanted to solve, I don't have to
pay a lot of attention to what they did do."

Well... do try to form some image of wheels rolling on asphalt
before driving on ice or joining the Foruma I circuit. The over
view of what you are simulating with statistics makes it much
easier.


As an undergraduate, I was continually beating my head against the wall
trying to imagine things like *why* they thought an electron should
repel itself, or *why* anybody expected there to be an ultraviolet
catastrophe. And if I asked anybody, the usual response was "Don't
worry about it. You won't use any of this crap once you're an
Engineer." After many years of further experience, I've realized I'm
not an engineer.

LOL.. So focus on the subatomic where the tools are more
valuable.


More of triple integrals so a flash of brilliance
gives instant insight where probabilty replaces "closeness"
or "earlyness". ( Howzat for temporal and spatial with a
down-home drawl? )


I'll have to see if that flash is forthcoming.


For a little railroad gedanken, all the above, is putting 10 possums
in a 2 possum sack. So the chapter written by Einstein
is to bad writing, as Shakespeare is to good writing.


Aye, he wrote inelegant proofs, as well.

I almost forgot 'simultaniety'. Einstein doesn't follow
with any development of probabilty so HUP is not
an issue. The two postulates are resolved formally
with time dependent Maxwell's equations.

They are resolved without paradox in this:
Observer dependent...
http://www.conformity.com/0102reflectionsfig3.gif
http://www.conformity.com/0102reflections.html
http://farside.ph.utexas.edu/teaching/em/lectures/node50.html

I am finding an extremely challenging exercise (for me) in here.

I really like this near-field/far-field thing. However, I am trying to
find a way to derive the equations given in here, and it took me a
couple hours this morning, and will probably take me a lot more time
because I am quite bad at getting Del X and Del Dot in spherical
coordinates. Now that I see this near-field/far-field thing, I MUST
see it to know how to believe it.

Yes. This is not an easy exercise. But it is worth as many attempts
as it takes to grasp it. When you do. A light will go on in you head
and you go "WOW that is how charged combs an pithballs keep
the refrigerator magnet from falling" This may be easier to see that:
http://en.wikipedia.org/wiki/Multiple_integral



...Constant speed of light:
http://physics.nist.gov/cuu/Images/alphaeq.gif
http://physics.nist.gov/cuu/Constants/alpha.html



Is there a reason to be excited about the fine structure constant
except its pretentious name? So it tells how fast the electron orbits
a proton in the lowest Bohr orbital as a fraction of c, right? Am I
missing something?

Free electrons have mass and Coulomb force too. They know
when they they are moving 0.999 times the speed of light
wrt an accelerator's cavity walls.

Read the roller skate gedanken and the music string page again.
Look at this:
http://physics.nist.gov/cuu/Images/alphaeq.gif
Can you find epsilon and mu in the roller skate gedanken?
( I hope so 'cause I forgot how ) Blush

Sue...





This is better because it is links to particular articles rather than
tables of contents.

Happy sums,

Sue...



Happy Products,

Jon...

.

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