Re: Understanding SR - simultaneity

Sue... wrote:
Spoonfed wrote:
Sue... wrote:
The Sorcerer wrote:
"Spoonfed" <good4usoul@xxxxxxxxx> wrote in message
news:1149118920.869337.71050@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| Androcles wrote:
| > Snipping will not make you right
|
| True.

So why do you try to convert other's to your faith?
You may succeed with a gullible moron such as yourself, but
not with anybody of intelligence. Somehow you are not "compelling".
Say three "Hail Galileo's" as a penance.
Androcles


Have you gone back and fixed your website yet, Androcles?

Tau = 1/Sqrt[1 - (u^2 + v^2 + w^2)/c^2]

You had three separate values for it before.

Forgive my big feet but this might be a good place to flesh out
something (a bit less religious) I am trying convey in another
thread.

What we may call an ?action~principle?..

Sitting down to learn at the feet of Sue.
ROFL Just finding common language.


uses a go or no-go
test. A collision happens... or it does not. It is perfectly suited
to operations of probability and statistics.

Absolutely.

There is no ambiguity about the meaning of simultaneous.

No? When two particles collide, is there no chance that one responds
slightly before or after the other? Can we ascribe meaning to
Heinsenberg's issue regarding T>E/hbar in this situation?
Later... in Hilberts space and Lorenz space.


You see debris or you do
not. There are no degrees of simultaniety. (Hilbert imaginaries)


This, I am not familiar with.
Some say "this ain't horseshoes"
Is there debris when automobiles almost collide?
Are photons almost absorbed ?

A collision is not when two bodies try to occupy the same space.
It is when bodies occupy the same space at the same *time*.


Precisely.

The problem is that all bodies occupy all spaces...

A superposition of schrodinger's functions?
I was refering the Coulomb field.

Swap the position of an electron and a positron
and the whole universe is going to know about it.


The electrical charges that comprise a material body are
infininitly large. See:

Is it the charges, or merely the effect of the charges, and how does
this infinitely large material body respond to a change in momentum of
the charge?
We only know the charge by its effects. If you could see
spray, but not the water sprinker, there are a lot of forms
you could imagine for the sprinkler's structure. So you
assume none of them. We know a sprnkling system
as a spary pattern that can be moved around the yard.
The rest is details for the hired help to trouble about.



http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html

We need a degree of freedom that a go/no-go test doesn't
provide.

We also need an explicit list of what comprises a go/no-go test.

Yes I was vague about that. Maybe it won't matter.

Rhut Row! Rough water ahead.
What
causes acceleration? A fall through a gravitational potential
describes a geodesic which seems to indicate no particular change of
energy, thus no radiation. Is this the same or different with
electrical potential? Quantum states of motion becoming available or
disappearing cause electrons to jump to new energy levels without an
associated change in kinetic energy. The result is radiation, or (if
you'll pardon the ambiguity of causality) absorption of radiation.

Suppose light doesn't depend on atomic absoption and emission.
Then we don't have to consider any of that. (for the moment)


Well, does light depend on the acceleration of an electron or proton?
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.

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."

....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."

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.

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.

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.

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.

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.

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.

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*

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.



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."

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.

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

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


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

I would *guess* they don't resolve in QM because
the nearfield effects of a coupling structure
can't be represented.
<< The difference between maxwell's equations in classic
field theory and quantum field theory is shown in red boxes.
The additional "red box" terms consist of magnetic vectorpotential
A, electric scalar potential PHI, material properties in vacuum
both permeability mue & permittivity eps.>>
http://www.wolfram-stanek.de/maxwell_equations.htm


Sue...



We can however take from it one great universal truth:
Embankments are a good place to put rail cars. :o)
http://www.bartleby.com/173/9.html

Sue...

.

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