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> Problem with the two slit experiment, Observing later
TRoc
Posted: Sep 13 2007, 07:06 PM


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Hi all,



Continuing forward...



I don't want to spend too much time pointing out apparent "miscommunication" between my posts, and the "summaries" provide by others, as LL mentioned.


This would be one problem:


Good Elf Posted on Today at 1:21 AM
QUOTE
This is where the story becomes divergent. TRoc wants (I think... I hope I am not misconstruing TRoc here...) to say that the continuous excitation excites a single atom over and over resonantly whereas I want to say that the individual atom is a "one shot" source of photons.... the quantum is a limited phenomenon ... it starts and it ends. This is not a mystery since this is all the energy that the single atom can hold. There is no internal source of continuous power. Further... the atom can only hold ONE and only ONE photon at one time for just one excitation demolition event. While in that 'charged up state" it cannot accept any further photons and the system is like a primed mousetrap ready to go off, just in need of a "trigger". While this situation is "holding" the atom in it's excited state it is reflective not absorptive. It has accepted one quanta and it can release only one quanta of that same energy, there is no current room for additional quanta.



The hope was in vain, I'm afraid. It would be easier for me just to say that, "laser technology" is adequately understood, and explained by the users (in experiments). I have nothing to "disagree" with there.


As for any "divergence", it was in the "translation" from me to you. You are asking me to "argue with the straw man". Giving a "one by one" explanation does not imply that there is only one participant, by itself. If, by my stating "in a large body" you did not get that I was talking about "very many" atoms doing this dance together, then, now, you can.


The "one by one" explanation was given, so that people can see that the NEXT RESONANT PHOTON already implies that the atom is in its relaxed state (the node), OR at the excitation peak (anti-node). Because "photons" have this same property (phase duality), the word "Resonant" means "phase matched": we have TWO ways to do this.


If the REAL value (QM's words) is the "peak" excited state, then this atom would ALSO be SIMULTANEOUSLY resonant with the IMAGINARY (the negative peak anti-node) part of an incident "photon". So, you are right, in that if a Real anti-node phase photon meeting a Real anti-node phase atom (in its first excited state peak) would cause "reflection" (as perfect as their phase match); the atom is "busy" for that caller. HOWEVER, if the Imaginary anti-node (peak) of a "photon" meets with same atom described above, then it IS NOT reflected. It exists in the "opposite phase-space": it GOES THROUGH the atom "undetected". It exits this space with the EXACT same phase as the NEW "photon" that was being created in the process of excite/relax dynamic. That is the superimposed, high intensity wave.


This does indeed happen, and is the cause for an increase in intensity due to superposition. I have offered an alternative to the "real vs. imaginary" phase space interpretation of QM". But you do NOT need to accept my premise, to believe that this is the way it happens, because it is also the same explanation that the experimenters are giving, that agrees with "current" new~QM.


This "feedback loop" is essential for the inversion process to happen. If this did not happen, there would be no conservation of energy, and the population inversion could not happen. That is why Mr. Bohr fully expected the first demonstration of the laser to FAIL; QM predicted NO interference.


There is a combination of stimulated, and spontaneous emission taking place. This explanation (stimulated) did NOT exist at the time the laser came into being, it GREW from experimenting with the laser.


The population inversion is a pure display of Resonance in action: the reflected AND the newly spontaneously created photons (same energy, different phase) INTERACT in the cavity UNTIL the "exit conditions" are met: ALL phases will "settle down" like the "black body curve", where we have a predictable "peak energy", if we know the starting parameters.


The " 1:1 " ratio will never get off the ground, so to speak.


The phases that can exit can be "EITHER / OR" anti-node peaks (real or imaginary phase space).


The phases that are "BOTH" (meaning Doppler shifted off "center" in one "phase space direction" or the other) do not get to leave the cavity.


They must literally go back to the "drawing board" and keep communicating until they "meet in the middle", and agree (resonate).

wink.gif


It is the "triple" potential, that can be divided disproportionately, so that one pair dominates the lone remainder. "Either + Or" trumps "Neither".


Positive and Negative can not co-exist in a "fuzzy" world, WITHOUT "Neutral".


Phase space is a fuzzy world.


A node, plus an anti-node, is only a half-measure; in an "all or nothing world", it equals "Nothing". "Dark~Energy"

biggrin.gif


ciao,

T.Roc


This post has been edited by TRoc on Sep 13 2007, 07:22 PM


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

I know Nothing. I looked all over to find it, but found it Nowhere. The funny thing is, it was right between 2 things, that I knew Everything about. It felt like forever, but really, it was no Time at all.

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TRoc
Posted: Sep 13 2007, 08:39 PM


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Hi all,



I was a little disappointed that no one responded to this link:

http://www.ece.nus.edu.sg/stfpage/elezhucx...olarization.pdf
Dielectric Materials
Chunxiang Zhu


We can simply use the electric dipole moment, based on the distance between a positive and negative equal charge.


There is our node and anti-node relationship.


They consider a dielectric slab. A regularly spaced lattice.


They talk about the "average" dipole moment, and the number of molecules per unit volume. The density of the potential absorbers.


They talk about "macroscopic" measurements, and local (internal) fields.


They say that these local fields "grow", when they are surrounded by "larger dipoles". Huygens' principle at work in molecules (macro collection of node-anti-node pairs).


They say that when these pairs are "spread out", such as in a gas, the local field (medium) is effectively the same as the applied field (EM wave).


They say that electronic polarization is "everywhere", because it is atomic in nature.


They remark that the speed at which the dipoles can respond plays an important role. And that the frequency of the applied field does too.


When the applied field is removed, this polarization vanishes. So does any "standing" waves. Standing waves can not stand alone.


The "fast response" of optical energies (visible band) is in the 10^15 - 10^16 Hz range. This is necessary for Talbot revivals. This is required to explain, that if we increase the "resolution" of a black and white fringe, we get colors. Specifically, we get a "red/yellow" pair, and a "cyan/violet" pair, and these DIRECTLY represent our "half-measures" of node to anti-node distance. "Conspicuously absent" (quote M. Berry) is green.


Resonance Theory predicts that "black and white" are just "magenta and green " that do not have the "intensity" to trigger a response in our (fantastically better than anything built by man) detector/cones. This has nothing to do with "perception", it is the "imaginary space" that was invented by Science, that contains the "imaginary explanation" that magenta is not "real".


This means that we are dealing with a non-linear phenomenon, by approximating "reality" with linear equations. Just like the "book" says.


They go on to say, that there 3 equations that combine (Clausius Mossotti) to explain the relationship between the macro, and the micro.


They continue to explain how large collection of node anti-node pairs (molecules) constitute (equivalent) to a larger pair, which must emit longer wavelengths. This matches the results: lower frequencies.


Then, they talk about "total polarization" being the sum of the different types, all interacting to produce the "final answer": end frequency matches energy expectation.



Let's move forward, and closely examine "the field", so that we can include it in a logical explanation for the SSE/DSE "foundational" results.


regards,

T.Roc



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

I know Nothing. I looked all over to find it, but found it Nowhere. The funny thing is, it was right between 2 things, that I knew Everything about. It felt like forever, but really, it was no Time at all.

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Confused2
Posted: Sep 13 2007, 09:06 PM


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LL ..significant post.. we must get back to it. TRoc's on a roll .. I don't want to interrupt.. (again!)

QUOTE (TRoc)
The field ..

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Good Elf
Posted: Sep 14 2007, 01:20 AM


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Hi laserlight, TRoc, Neil farbstein et al,

QUOTE (laserlight)
Care to tackle an explanation regarding my prior post re a laser beam not expanding as an omni-directional spherical wavefront?
It is a very cleaver case of a "phased array" in a field of "active antennas". The resonant cavity is one way to form a phased array by the population inversion followed by the "Mexican Wave" progressing along the tube reinforced by the boundary conditions where the walls are forced nodes and each atom is a microscopic dipole antenna.
Wikipedia: Phased Array
The phased array is a one shot in this case rather than simply continuous "beam steering" by modifying the delays in various antennas using line delays. In the laser tube the "line" is the traveling wave passing through the tube which triggers each primed atom into a directed one sided pulse along the direction wave.

The tubes side lobes are suppressed by having a spatial filter at the exit to the tube to reduce all but the primary transverse mode or even several spatial filters. These will suppress the side lobes even more. It is also conceivable that special pulse shaping is used in the military case to enhance the beam characteristics.
QUOTE (TRoc)
As for any "divergence", it was in the "translation" from me to you.
Apologies if there is no disagreement and I am being a bit too pedantic. Sorry about that. You all know I am "obsessive".

Regarding charge polarization, I know it is heresy but who still thinks that elementary charge is 'static' and not "dynamic" as in the case of Williamson and Van Der Mark? Static fundamental charge implies that the property of charge relies on two separate mechanisms for formation.... there would be instantaneous fields that "create" charges" in free space from nothing and the existence of charges in particles. On my mind there seems to me that we need to explain charge with a single explanation of topologically wrapped electromagnetic fields which are dynamic in their 'internal" nature... what do others think? What do you think TRoc since I am unsure that you have made a statement on this concept. I think that the charge is not fundamental and it is the electric field that is fundamental and standing waves can produce "topological charge" even in atomic partivcles. That the "wrapping" internal to fermion particles of photons result in charge , parity and the evolution of time as previously discussed... this is CPT-Lorentz Symmetry and related to stable soliton production.

In Williamson and Van Der Mark's Paper....
User posted image
and also...
User posted image
...Click to enlarge...
Where we have the Hubius Helix in there as an internal structure. I think the photon 'spreads" internally and that this may be signalling additional physical dimensions.
User posted image
...Click to enlarge...
Taken from "The nature of the electron" by Qiu-Hong Hu

There would need to be internal structure not necessarily seen in these illustrations to support spreading such as "standing waves" and "diffraction". The appearance of mass is also the appearance of time and space and all particle properties. The absence of time and space and mass seems to me to be the initial state of our Universe (before the "Big Bang"). Correct me if I am wrong but take away the property of mass and we have lost the property of time since massless particles seem to always travel at the speed of light. A universe entirely composed of light and devoid of mass could have no observer ... all observers need mass to have time to make observations. Anything in that reference frame can make no observations of any Universe. All that can be done to that frame of reference is to observe it. So this is a unique "condition"... ontologically nothing can come "before light".... this has philosophical implications even in our Universe.... Agreed?

Cheers

This post has been edited by Good Elf on Sep 14 2007, 02:02 AM


--------------------
"Aa' menle nauva calen ar' ta hwesta e' ale'quenle"
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Laserlight
Posted: Sep 14 2007, 01:22 AM


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Hi TRoc,

Good stuff!

QUOTE
A node, plus an anti-node, is only a half-measure; in an "all or nothing world", it equals "Nothing". "Dark~Energy"


A half wave cannot be naturally "generated" as a photon, since it cannot propagate
away from a source. A half field would represent a pulsed "DC" component.

It could, however, possibly represent a localized oscillating "field"
possessing a DC polarity component. Such a field could temporarily "change" the
dipole moment/alignment of an atom, making it oscillate/jiggle from its "normal" polar orientation.

JMHO,
LL

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Neil Farbstein
Posted: Sep 14 2007, 01:36 AM


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QUOTE (Good Elf @ Sep 14 2007, 01:20 AM)
Hi laserlight, TRoc et al,

QUOTE (laserlight)
Care to tackle an explanation regarding my prior post re a laser beam not expanding as an omni-directional spherical wavefront?
It is a very cleaver case of a "phased array" in a field of "active antennas". The resonant cavity is one way to form a phased array by the population inversion followed by the "Mexican Wave" progressing along the tube reinforced by the boundary conditions where the walls are forced nodes and each atom is a microscopic dipole antenna.
Wikipedia: Phased Array
The phased array is a one shot in this case rather than simply continuous "beam steering" by modifying the delays in various antennas using line delays. In the laser tube the "line" is the traveling wave passing through the tube which triggers each primed atom into a directed one sided pulse along the direction wave.

The tubes side lobes are suppressed by having a spatial filter at the exit to the tube to reduce all but the primary transverse mode or even several spatial filters. These will suppress the side lobes even more. It is also conceivable that special pulse shaping is used in the military case to enhance the beam characteristics.
QUOTE (TRoc)
As for any "divergence", it was in the "translation" from me to you.
Apologies if there is no disagreement and I am being a bit too pedantic. Sorry about that. You all know I am "obsessive".


Cheers

Nobody minds.


--------------------
Life is a tale told by an idiot full of sound and fury; signifying nothing...Tomorrow and tomorrow and tomorrow, but tomorrow never comes. -William Shakespeare.
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TRoc
Posted: Sep 14 2007, 02:48 AM


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Hi all,



We have seen all the input from the "giants", whose shoulders we wish to collectively stand upon. It is a fantastic variety of solutions to the equally fantastic variety of problems. Question, experiment, answer... question, experiment, answer...


The Garden is Wondrously large, and varied. Literally "one of everything", for it contains all efforts. We humans have a bad habit of keeping specimens that we have decided are "weeds", for "reference" (nostalgia).

Then, we teach it in the order in which it was "discovered", to show the steps that were taken. If, a more "general" discipline is sought, the student's understanding of Physics may just have ended on a "node" laugh.gif I think that this goes on quite a bit.


This is just an observation; I seek no remedy for the method. The bottom line is that, if we had a GREAT answer for the students question, in other words, some "unified way" to explain all phenomena, it would be taught FROM THE START, so that, even after one's education had ended, you could still apply those Fundamental Principles that you learned (and ended at any level) to understand "new" events.


We do not have such an answer.


We do have MANY very, VERY good ones. The biggest problem, is that they are growing in the wrong "order". They need to be re-organized, and FREE OF WEEDS. Weeds can be anything that had once been "assumed" to be "a guarantee", but later proves to be simply FALSE.


We can do mentally, what can not be done "literally". We can "imagine"; we can "postulate"; we can "inquire". The old saying, that "if I knew then, what I know now, ...".


We CAN easily IMAGINE going back to 1800's, armed with what we "know now", and RE-ASK the fundamental questions. This is the equivalent of "a classical explanation" of the "quantum reality"; it's not a new idea.


Not just "OBEY" the fundamental laws, but go INSIDE the minds that wrote them. There is a version of Buddhism that does this same thing.


HOW would WE "write" these laws? What words would WE use, that the original authors (who did NOT know what we do) would not have?


Great example: "Thermo-dynamics". Because of the "words" they use to describe the phenomena, we are left with the need to "interpret" this into our "modern" tongue.


Later, we learn that "heat" is not a "thing". (more an action)


So, it seems, we were obeying the law of Nothing Dynamics. Not so bad, considering that we later define "what exists between energy", as "Nothing", a zero singularity. [if "nothing" exists between 2 oscillators, they are not separate/they have NO difference]


If heat is now understood as "the difference" between 2 oscillations (energy levels), and the primary result is that the higher/hotter energy always transfers in the direction of the lower/colder energy, then THIS is our Fundamental Dynamic.


If we know now, that frequency is THE parameter that we can measure the best, and it is also a DIRECT connection to the energy level, then Frequency is our Fundamental Parameter.


The word "beat-frequency", just means "delta f", or the "difference" in those values.


We have evidence that matter behaves like waves, at the atomic level. (noticeably. Long waves are too slow to see)


At the time of the founding of these Thermodynamic laws, this was not understood.


They applied statistical analysis to "measure" a body of gas. This was done as "oscillators" (having frequency). To cut to the chase, one of the first "amendments" to Thermodynamics, is the "Equipartition of Energy".


At equilibrium, we have the LIMIT. In general terms, all of the oscillators have "settled down", to integer wavelength differences. No "beats". How can I say this, if a beat-frequency is "delta f"? Because "harmonics" fit in a nested curve set; if there is no difference in the fundamental (1st mode) frequencies of 2 oscillators, then there will be no difference in their harmonics.


This has a simple "visual", with concentric circles; the Unshifted Doppler "metric".

The Monochromatic Perfect Circle, and its Harmonics.


If we push 2 of these together (of exact same "rate" between lines), all of the intersections cross at "un-differentiable" points.


If we start with 2 DIFFERENT frequencies (rate between lines), then we will clearly see the difference, although, it will cross different lines, in different ways. You may say, "wait, that sounds hard to model", and it could be. Euler found a way through it, by taking only the "correlated" parts, the "coincidence of blows".


But, that was still when Music had not been "quantized". The intervals were not the same; not isotropic; not able to differentiate to the "monochrome", as it were. wink.gif


He ended with just a much more complex version, of Pythagoras' conclusions, 2000 years prior! The INTEGER only approach, using the "harmonic series" was doomed. Why? Because WAVES are "complex", meaning "more than two components: you MUST have DISTANCE/TIME (wavelength), CYCLES/TIME (frequency), and their PRODUCT is CONSTANT. That's it.


If that CONSTANT has no integer square root, then it has an irrational relationship.


Fortunately (for studying patterns) light and sound fall into that category. Solve one, you solve them both.


It just simply extends from the fact that if we multiply an integer and an irrational number, then we will always get an irrational number. Translated into wave mechanics, we are saying that the distance parameter, when measured in "integer wavelengths", is being put into "natural units". Again, in music and optics, this is the meaning of the "fundamental frequency", so that "natural units" of THAT value are being measured.


In terms of energy, we have just created a problem: terming what came before the fundamental as ZERO. And what is between the "real" peaks, and the "imaginary nothing" that separates them is "zero" too.


However, measuring against the fundamental length is NOT bad, in itself.


Remember, we have THREE parameters: distance, time, velocity.


So, it is more important to state that if we measure from ONE integer, the other two parameters will be IRRATIONAL. Time is that integer parameter, that is ubiquitous to all experiments, that have a "start" and "end".


We have the possible answer that, "over every possible fractional unit of time", energy (the complex term) will have this inverse relationship: a distance parameter that "fluctuates" in space, and a cycle parameter that "jumps" in time.


Lets go back to the visual of our gas-medium in an equilibrium state. We'll follow our start, that this means "heat transfer" is no longer happening, there are no beat-frequencies being exchanged. The statistical knowledge that we have of this is very good. This is the "primary" evidence: Equipartition of Energy = isotropic lattice.


Imagine each atom as a relaxed state oscillator, at "rest" in terms of the average positions of its neighbors, and so being "evenly distributed". Each atom is a nested group of circles, that are related by an integer expansion of their radii. This is the Doppler set of circles, unperturbed, or shifted. Because of the linear/integer expansion of the radius relationship, these nested circles are directly compatible with a metric that is also integer based, namely "1 meter".


So, the medium has a great many of these concentric circle sets, equally spaced out, and their polarization states are independent of each other. The real deal is in 3D, but we can look at just the plane level with the slits. As soon as we have "light incident on this macro field", the field responds. THIS DOES NOT STOP DUE TO ANY CHANGE IN FREQUENCY OR ATTENUATION.


One thing that is definitely happening "in the 1 photon regime", is that the time between "pulses" is REGULAR. Because the relaxation time of the medium (field) is finite, and greater than this "pulse interval", we end up with a "modulated fluctuation pattern", that swings between these limits.


Recall the videos that I linked showing "cymatics": we could see the frequency specific fluctuation pattern of the independent bodies of "absorbers". It is not likely, that the same grain of sand will maintain even an "approximate" consistent position, as the frequency is changed (modulated).


So, in our lattice, in the energy regime of "one photon", we are going to get "one electron" doing the job of "absorb/re-emit". Once this job is performed, it DOES NOT take up its' original position, it gets "recycled" into near the "end of the line", because the "line" (fluctuation pattern) is frequency dependent too.


Because this body, or lattice, of gas is NO LONGER in equilibrium, it is COMMUNICATING via "heat", or "beat-frequencies". The WHOLE body contributes to the "revival" of this energy level. The "vacuum" does not contribute, it does not exist. THE MEDIUM CONTRIBUTES the energy, so that our observed conservation takes place.


Because of the difference in the modulation, between the relaxation (thermo limit) and the next input of energy, the "lead atom" (front man for the Talbot carpet) CAN NOT have EXACTLY the same energy as the one it replaced, and will send (via a difference in reaction) the next "photon" to a different place on the (envelope/fundamental dependent) same fringe pattern.


The reason that the pattern is still completed the same, as if we had sent all of the photons "back to back", is the timing of the envelope. It is based on "equal division" of the fundamental frequency. The field is responding to that input the WHOLE time, only the RATE in which the pattern can be "seen/perceived" changes. An equal division of the fundamental delivers a precise change in the unit of time to measure said rate (frequency) with. The original pattern was a rate over time, and the "one at a time" DSE is just the "same rate in more time". The period changed (the interval between events), but not the rate.


I went past the point that we needed to right now, just so that you can see ahead of time. that this is the ONLY logical answer, to the entire set of questions.


When we have the right answer for "basic phenomenon A", we will be able to also answer "complex phenomenon B" with the same method and model.



After all that, now I'm going to show the "reading list". As usual, it is not short; and it is not trivial. I do not have the time for a "full book report" on each one, and the references of each. If you want to know the way, especially in how it relates to the models that YOU personally (each reader) can relate to. We are all different in that respect.



HOT off the press, still to be published, "experimental confirmation":


Doppler Asymmetric Spatial Heterodyne Spectroscopy (DASH): Concept
and Experimental Demonstration

Christoph Englert, David Babcock, and John Harlander
Applied Optics - accepted 13 August 2007

http://ao.osa.org/DirectPDFAccess/0195CE70...FTOKEN=71488311
(this is free only for a short time; link may not work)

QUOTE
To date, space based Doppler shift observations of atmospheric emission lines have been made from a few research satellites to obtain wind information. Since the measured Doppler shift contains only velocity information along the line of sight, measurements of horizontal wind speed and direction require the observation of the same location using two perpendicular viewing directions. 

..

A limitation of stepped Michelson interferometers is that the isolation of a single atmospheric emission line typically requires an ultra narrow pre-filter with all its attendant difficulties and reduction in throughput. Further limitations are that the interferogram is only sampled at a few (typically four) optical path differences and instrument drifts cannot be monitored simultaneous with every atmospheric measurement, since only one line may be in the passband at any time. 

DASH can be considered a combination of stepped FTS and Spatial Heterodyne Spectroscopy (SHS).

Typical atmospheric wind velocities cause atmospheric emission lines to be Doppler shifted by only a few parts in 10^8. This small wavelength shift results in a small frequency change in the interferogram as recorded by an SHS, DASH, or FTS instrument. Fig. 1 shows an ideal interferogram of a single, infinitely narrow spectral line versus optical path difference and the interferogram of a slightly Doppler shifted line. As is well known, the small frequency change in the interferogram has a negligible effect for small optical path differences; however, at longer path differences it appears predominantly as a phase shift. The main objective of DASH is to measure this phase shift, thus it is sufficient to measure the interferogram at high optical path differences. Note that the brightness of the interferogram and the fringe contrast contain information about the density of the emitter and the line shape, just like in the stepped FTS case.



QUOTE
Line broadening affects the envelope of the interferogram; a broader
line corresponds to an envelope that decreases more rapidly with increasing path difference.  In general, this envelope function causes the interferogram contrast, or visibility, to decrease with increasing optical path difference as shown for a purely temperature broadened line in Fig. 3.  This effect competes with the increasing phase shift for increasing optical path difference (see Eq. (1)) so that there is an optimum path difference offset for which measuring the phase shift and thus the Doppler shift is most sensitive. We find this optimum path difference by
maximizing the envelope of the difference between the interferograms of a Doppler shifted and non-shifted line (see Fig. 3). 



QUOTE
Using Eq. (7), the phase term can now be calculated from the ratio of its imaginary and the real part :



QUOTE
After subtraction of 2πκ0x+Φ0, which is also called the zero wind phase, we get the phase shift δϕ0 caused by the Doppler shift for this particular line. The speed between the emitter and the spectrometer can now be calculated using the phase shift δϕ0 and Eq. (1).



Note: this is what I mean by "lateral observers", measuring shifted velocities, AS seen by the "central" observer (axis ; a preferred frame). Following the diffraction angles back to the slit, you find the phase shift (in frequency) that matches the RI change in velocity. (RI is based on a particular frequency, so that its' velocity is "adjusted" to c , essentially)


QUOTE
In order to avoid aliasing, the highest fringe frequency may not exceed the Nyquist frequency, that is the number of fringes across the detector width may not exceed the number of detector pixels divided by two. This example illustrates that the heterodyning aspect of DASH is essential for achieving well separated fringe frequencies that can easily be sampled..

.. well separated also ensures that the envelope of the beat pattern from 2 or more lines in the passband, has a periodicity that is significantly smaller than the width of the detector.

This way the interferogram sampled by the detector can never be confined to a node or zero point of the beat pattern envelope..


(like the "1 at a time photon" from a laser beam)


QUOTE
The interferometer was vibrationally isolated from the optical bench and a top cover was used to suppress ambient and stray light contributions.


(because they are SERIOUS about accuracy)



http://arxiv.org/PS_cache/chao-dyn/pdf/9906/9906005v1.pdf
FINITE TIMES TO EQUIPARTITION IN THE THERMODYNAMIC LIMIT
J. De Luca, A. J. Lichtenberg, S. Ruffo
31 May 1999

QUOTE
We take the initial energy to be either in a single mode γ or in a package of low frequency modes centered at γ and of width δγ, with both γ and δγ proportional to N.  These initial conditions both give, for finite energy densities E/N, a scaling in the thermodynamic limit (large N), of a finite time to equipartition which is inversely proportional to the central mode frequency times a power of the energy density (E/N). A theory of the scaling with (E/N) is presented and compared to the numerical results in the range 0.03 ≤ E/N ≤ 0.8.



QUOTE
The mechanism of a transition to more rapid energy transfer is that for energy above a threshold E ∝ N−1, interaction of neighboring low frequency modes will lead to a local super-period beat oscillation, of period TB ∝ N2/γEγ ,
that is stochastic. At a sufficiently high energy a resonance with high frequency modes leads to a transition to a fast diffusion regime which occurs above a critical energy E = Ec,  independent of N.

..

In this paper we examine the relationship between initial conditions for which the energy is placed primarily in a single mode γ, which we call “mechanical” initial conditions, with initial condition for which the energy is placed in a finite δγ package of neighboring modes with δγ ∝ N, which we call “physical” initial conditions.

..

The main numerical tool we use is the calculation of the effective number of modes
n_eff containing the energy.

..

(Fig. 5), which indicated an extra volume filling factor, proportional to √N, when the
energy was placed primarily in a single low frequency mode, typically γ = 3. In this case the primary driving frequency is a beat B ∝ γE/N2, with γ = 3, such that the time for transferring energy is much longer than in the present situation. This allows the filling of the low frequency modes by successive excitations (see ref. [1]) to manifest itself in the additional √N dependence.

..

In the following we present an approximate theory of Hamiltonian diffusion to explain, qualitatively, the power law behavior at low energy densities. We start by assuming that there is an effective number of low-frequency modes δk that are responsible for stochastically transferring energy to the high-frequency modes, leading to equipartition.

..

Because of the nonlinear couplings among the low-frequency modes, the frequency of these modes is corrected by a beat that we approximate in the following way.

In (8) and below we set N + 1 ≃ N (large N) except where it appears in the selection rule. ¿From (3) ωi ≃ πi/N, for low frequency modes, and taking the beat frequency B, between ωi and a neighboring mode, to be of the order of the nonlinear frequency shift, we obtain, for any i (with i ≪ N), ..

..

As in our previous work [1] the notation h1 and h2 explicitly indicates that the energy transfer occurs only between low frequency beat oscillation and high frequency mode difference oscillations through the Arnold diffusion mechanism.


Since δk low frequency modes, assumed to have energy, couple to δh high frequency modes with δk = δh, the cross-couplings imply each high frequency mode is coupled on average to δk/4 low frequency modes. There are phases in the low frequency mode beat oscillations and in the high frequency difference oscillations that can affect the Arnold diffusion. This has only been studied for exponentially slow diffusion [12]. The effect of these phases when more than one driving term exists, for the case of strong Arnold diffusion, B <∼ δωh, has not been studied.

..

Furthermore, we expect that as the energy in the high frequency modes increases, other pathways become available for the energy distribution among the modes, to further justify holding the number of couplings constant in the integration.

..

Furthermore, n_eff is related to the evolution of the energy in the individual modes in a very complicated way.   These dynamics lie beyond a simple mode-averaged theory. We also emphasize that the theory depends on having non-exponentially slow stochastic diffusion to high-frequency modes, being driven by local mode-mixing stochasticity among low-frequency modes [1].




Further reading on Arnold Diffusion:

http://www.turpion.org/php/full/getFT.phtm...6_355&x=107&y=5
ARNOLD DIFFUSION AND THE D’ALEMBERT PRECESSION PROBLEM
V.MASTROPIETRO
Universita’ Tor Vergata, Roma October 30, 2001



regards,

T.Roc


This post has been edited by TRoc on Sep 14 2007, 02:55 AM


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Confused2
Posted: Sep 15 2007, 06:40 PM


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Hi TRoc and all,

Do you agree..

At various stages I think at least some of the regular posters have agreed that the pattern is the same as the superposition of two sinewaves. Then it goes horribly wrong .. instead of trying to explain how/why the pattern is indeed the sum of two continuous sinewaves there is a tendency to try to explain why this cannot be true and then go on to discuss other results and other experiments.

Best wishes - C2.

This post has been edited by Confused2 on Sep 15 2007, 06:48 PM


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Laserlight
Posted: Sep 15 2007, 07:57 PM


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Hi C2,

QUOTE
At various stages I think at least some of the regular posters have agreed that the pattern is the same as the superposition of two sinewaves. Then it goes horribly wrong .. instead of trying to explain how/why the pattern is indeed the sum of two continuous sinewaves there is a tendency to try to explain why this cannot be true and then go on to discuss other results and other experiments.


WHAT? I think everyone has agreed that the DSE interference pattern is a
wave superposition effect. IMO, the argument has to do with the "mechanics"
of the mechanism, and the nature of photons.

This argument has been ongoing for 200 years, we are just the latest who are
trying to bring in new information into the argument, that didn't exist previously.

A "conclusion" must satisfy ALL possible results/variables. If one fails the test,
then other alternatives must be explored.

LL

This post has been edited by Laserlight on Sep 15 2007, 08:00 PM
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Confused2
Posted: Sep 15 2007, 08:36 PM


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Maybe I missed out a few crucial words .. two continuous sinewaves of a single frequency
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Good Elf
Posted: Sep 16 2007, 02:17 AM


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Hi Confused2, TRoc, "THEY", "THEY2" Laserlight, janrinze, Jal, Montec, yquantum, StevenA, "Why Not?", Siau, Neil Farbstein, Terry Giblin, et al,

QUOTE (Confused2)
At various stages I think at least some of the regular posters have agreed that the pattern is the same as the superposition of two sinewaves. Then it goes horribly wrong .. instead of trying to explain how/why the pattern is indeed the sum of two continuous sinewaves there is a tendency to try to explain why this cannot be true and then go on to discuss other results and other experiments. [...] Maybe I missed out a few crucial words .. two continuous sinewaves of a single frequency
While I "agree" that for two slits and for infinitely thin "ideal" pinholes/slits the result "resembles closely" interference between two continuous sinewaves... The truth is that there is a fine detail involved in the pattern due to the finite aperture of the pinholes/slits. There is a complex transform plane as shown in those devices I have linked previously between a "secondary source" and the screen "image".... The transform plane.
User posted image
... Click to enlarge...
In this case the input plane is composed of an semi-infinite number of individual secondary sources which are all self-interfering.... photon by photon of monochromatic light from the LASER.

Pinholes (or slits) are just a limiting case of "lenses" with an extremely small aperture with all the optical distortions that optics of pinholes introduces. The pinhole is a camera obscura with a highly defined optical transfer function. This "theory" (if you can call it that) has no generalization to extended slits/pinholes or arbitrarily placed pinholes/slits in three dimensions. It cannot be simply extended to lenses either. This simplistic two wave concept explains nothing. It is easy to explain to children... that is its "virtue". I am expecting more from this group than this simple "explanation".

IMHO... This phenomenon can only be answered by harmonic solutions on the surface of a sphere or cavity of a resonant phenomena in space of standing waves. These standing waves are related to the physical "shape" of an associated connected cavity space.

The next point is there are the standing waves that need to have an answer... two progressive waves interfering produce a progressive wave solution... the real answer is not a progressive wave... it is a stationary pattern involving Talbot Carpets which are spatially non progressive. These patterns are a resonance not waves lapping on the beach. The actual phenomenon resembles this effect shown in zephir's electron diffraction image...
user posted image
Slight modification is required for photons and their spreading. In the same way that this animation shows one electron interference through the wave passing through both slits the photon also passes through both or (all) slits... seeking all paths.

The next point is this/these patterns of all kinds, be they formed from one pinhole, two pinholes, three pinholes .... million pinholes ot any arbitrary size... placed in any position on the outside of an arbitrary shaped "cavity", with reflections and so on, have a general solution that is "per photon".... one photon at a time... even if they are separated by long periods in time. The standing waves are produced by some quantum effect that is not accounted for by the two wave theory. The patterns are due to geometry and to frequency of the photon... a combination of the two... Each photon frequency has a different effect and it is dependent solely on the physical geometry of the cavity. They form a superposition of possible solutions. You do not need two different sources of waves or two waves created by two separate photons to produce these standing waves.... each individual photon does it all by themselves.

Then we have the question posed by the original problem... "Observing later"... referring to the Delayed Choice Quantum Eraser Experiment. The solution I have proposed is a "one stop shop" that answers all of these points together .... no piecemeal answer but a full mechanism that provides a framework that is an answer to this quantum quandary. The answer does not involve only the particle solution but is mostly concerned with the wave solution.... I have demonstrated practically why quantum theory does not answer these problems and why an extended wave theory does explain these issues.... Why there are those fine excellent patterns and why holograms are not a chaos of random photons but a highly "orchestrated" and exacting interference pattern of standing waves in space. To the "observing later" question... the relativistic interpretation of the photon "in frozen time" and "contracted and rotated space" solves the quandary between entangled photons apparently having a "back action" back through time. The "fiction" is related to our frame of reference which discriminates between the single event which is happening is different regions of space at different times... when to the photon these apparently separated events are simply the one event that is neither distant nor separated in time from it's entangled partner.

Cheers

This post has been edited by Good Elf on Sep 16 2007, 02:33 AM


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TRoc
Posted: Sep 16 2007, 05:54 AM


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Hi all,



C2, you are asking for the affect of 2, same phase cycles, correct?



http://en.wikipedia.org/wiki/Pendulum

QUOTE
Perhaps based upon the ideas of Galileo, in 1656 the Dutch scientist Christiaan Huygens patented a mechanical clock that employed a pendulum to regulate the movement.[7] This approached proved much more accurate than previous time pieces, such as the hourglass. Following an illness, in 1665 Huygens made a curious observation about pendulum clocks. Two such clocks had been placed on his mantlepiece, and he noted that they had acquired an opposing motion. That is, they were beating in unison but in the opposite direction—an anti-phase motion. Regardless of how the two clocks were adjusted, he found that they would eventually return to this state, thus making the first recorded observation of a coupled oscillator.[8]



( And, the first matter wave resonance. Think of the "eigenstate", which represents the coupled systems' most energy conserving mode. In this case, the "setting" of the clocks is the perturbation, and the relax time is the period that it takes for them to become "beat free", no difference in their cyclic rate. )


http://en.wikipedia.org/wiki/Odd_sympathy

QUOTE
Huygens originally believed the synchronization was due to air currents shared between the two pendulums, but he dismissed the hypothesis himself after several tests. Huygens would later attribute sympathetic motion of pendulums to imperceptible movement in the beam from which both pendulums are suspended. This idea was later validated by researchers from the Georgia Institute of Technology who tested Huygens' idea. [1]

Using instruments capable of registering movement too small to have been measured in Huygens' time, the Georgia Tech researchers chronicled the nature of the forces at work on the supporting beam. They found that if the pendulums are moving in the same direction, together they tend to move the beam the opposite direction, giving rise to frictional forces that resist motion in the same direction. If however, the pendulums are moving in opposite directions, these forces cancel each other out, causing the beam to remain motionless. Thus, motion, in this example, tends to be perfectly asynchronous.



If there is a medium of communication between the 2 oscillators, like in the example above, and their degrees of freedom are in 2 dimensions, the "movement" will be asynchronous; the energy will take up the fundamental form of node/anti-node/node, meaning from the center, out. (in both directions).


In the "photon", or quanta of energy, the result of the superposed resonant sine waves puts a PAIR of peaks in the same space and time. This causes the immediate creation of a node/zero point that must exist between them, so that they have separate existence. This can be interpreted either as "new photons", as a Doppler shifted "fundamental" frequency, or as Huygens principle.


The amplitude of the EM wave is interpreted as the electric field. However, because of the "symbiotic" relationship with the magnetic field, and their 90 deg geometry, it has been established that these definitions are only valid for particular frames. I do agree with the premise that charge and mass are secondary effects of the fundamental cause.


The EM wave can be modeled as a helice, and the property of phase singularities, the "vortex", is too. This is a Fundamental pattern: it is from this, that energy is transferred from "nothing", that consists of a barely perceptible redshift, by the absorber/emitter bodies that populate the "space" in question. A tiny, "infinitesimal" contribution by every "particle" in the Universe.



So, your question C2, which I think was too vague to give a definite answer, sounds like the SINGLE slit question. For the SSE, that is a true statement. For the DSE, that is not true. We went over this, and I thought were in agreement.
It can not answer the "1-at-a-time" question/dilemma, anyway.


To answer your question means we have to go though the "monochromatic" issue again. It was laid to rest. A single frequency has all its eggs in 1 basket: it ONLY exists on the zero or the y axis (infinitely). In 3D, it is "infinite curvature"; the loop. The single frequency, that had only ONE anti-node, between 2 nodes, is not moving, by definition. This is the orbit. If it is moving at c , then we have RDS in affect, and the frequency can not be monochromatic throughout the envelope.


The extremes, and the mean; the positive, negative, and neutral. We need three bodies for some geometric stability. 2 " r 's and 1 pi " (or 1 real r , 1 pi, and 1 imaginary phase -r ).


Was that any help?


regards,

T.Roc


This post has been edited by TRoc on Sep 16 2007, 06:14 AM


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Confused2
Posted: Sep 16 2007, 08:28 AM


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Hi TRoc, Good Elf, "THEY", "THEY2" Laserlight, janrinze, Jal, Montec, yquantum, StevenA, "Why Not?", Siau, Neil Farbstein, Terry Giblin, et al,

QUOTE (TRoc)
The extremes, and the mean; the positive, negative, and neutral. We need three bodies for some geometric stability. 2 " r 's and 1 pi " (or 1 real r , 1 pi, and 1 imaginary phase -r ).


I don't think this is going to make any sense to me unless you give a 'worked example'.

Something like ..
A hot filament emits a photon ..
de dum de dum
two slits
de dum de dum
and so makes a bright spot on a photographic film at point 'X'.

Best wishes - C2.

Good Elf .. I don't think camera and telescope manufacturers take into account 'standing waves' .. does this lead to a problem or have I missed something?





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Good Elf
Posted: Sep 16 2007, 10:17 AM


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Hi Confused2, TRoc, "THEY", "THEY2" Laserlight, janrinze, Jal, Montec, yquantum, StevenA, "Why Not?", Siau, Neil Farbstein, Terry Giblin, et al,

QUOTE (Confused2)
Good Elf .. I don't think camera and telescope manufacturers take into account 'standing waves' .. does this lead to a problem or have I missed something?
You are right... "It" (standing waves) is not a problem for camera and telescope manufacturers... This is like saying that the Theory of Relativity is not a problem for Bricklayers. It is true but missing the point. While it it quite right to say these kinds of enterprise would not necessarily benefit from an understanding of quantum theory or Relativity it is of prime concern to Physicists. It is physics that must account for the phenomenon observed.

A Theory of all phenomena will include this fact and it will be able to be incorporated in a complete Theory of Everything seamlessly. For me the spatial standing waves "fits" aspects of Wheeler Feynman Absorber Theory.
user posted image + user posted image = user posted image
These are standing waves but you see advanced and retarded waves here. In the "real world" you do not "see" advanced waves. This is because they are waves that are running in the opposite way to causality. Still they are there and are producing standing waves... this is all the matter that exists in our Universe.... the matter waves are stationary in time but represent the confluence of advanced and retarded waves in space.... our space. What we are witnessing is the effect we are seeing in that animation...
user posted image
What you see is the influence of matter as "stationary spatial states"... those matter standing waves... and the causally related retarded wave version of propagating and spreading photon packets which are forced to move under the influence of the matter waves. Each frequency of photon interacts with this matter wave field in a different but predictable way. We know that simple law for a double slit. There is another more competent solution and it deals with the wave equation for electromagnetism... an exact analog for the Schrodinger Wave Equation.
User posted image
... and...
User posted image
... Click to enlarge...
What we have here is a general solution for cavities with waves rather than cavities with particles.

Recall that a single photon cannot produce standing waves by "bouncing around a cavity resonantly" ... the single one off photon goes directly from source to sink... Yet this is a "resonance". The standing wave is already there defining the space and to capture the energy of the propagating photon. The DSE is as much of a cavity as is the resonating bell but it reacts in accordance with the advanced waves.

Everything is in a state of "resonance" even if it is only a one shot wonder. This is the "secret" behind everything. The cavity is always there and photons "feel" the space as a resonance without actually having to personally probe all the space as a particle. These are the "interferences".

Wheeler Feynman Absorber Theory "fits" Cramer's Transactional Hypothesis and these show a way to interpret events occurring in the Delayed Choice Quantum Eraser Experiment when we incorporate Special Relativity. It is the process of seeking a consistent view not a series of disconnected facts.

Milo Wolff has a similar theory but I disagree in the details about the internal energy flow of particles (See Williamson and Van Der Mark's paper). Still it is an allied concept. To me particles connect like Falaco Solitons in a swimming pool. The cores are not "bobbing up and down" but spinning. This creates its own space in which to move... additional dimensions derived from compact spatial dimensions being inflated. These interferences are "measured" using photon waves... they diffract through them the same way as they diffract through other matter such as X-Rays in crystalline matter... Bragg's Law... but the fine detail and cavity resonances are lost due to the nature of those interferences in the space being so much shorter in wavelength than light. The way photons behave with these interferences is as in a reciprocal space.

Cheers

This post has been edited by Good Elf on Sep 16 2007, 10:34 AM


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Confused2
Posted: Sep 16 2007, 12:31 PM


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Hi Good Elf,

Looking at the Zephiry gif..
user posted image

Taking it 'as drawn'..

we see about 50% of the wave is reflected .. with 'real' slits it would probably be closer to 99%. Whatever 'wave' that doesn't go through the slits must be reflected because if it was absorbed it would be 'game over' for that particular photon. This does raise the question of .. what happens if we paint our barrier black .. why does it still play the part of a reflector?

Once a photon has been detected at the screen there is the problem of all those waves that were reflected from the barrier. Somehow the whole wave structure has to be cleared up. I don't see that it would be enough to throw the process into reverse from the point of detection because it's in the wrong place to cancel the waves from the source .. the cancellation has to happen from the source.. you agree? No part of the wave that is not 'local' to the point of detection can know a detection has occurred .. unless you have some sort of non-local phenomenon to connect the wave that is reflected to the wave that passes through the slits.

QUOTE (GE)
The standing wave is already there defining the space and to capture the energy of the propagating photon.

I'm not sure whether this is intended as an alternative or as part of Wheeler-Feynman. We can certainly agree that the DSE effect exists .. to say "Space does it" seems to be rather ducking the issue .. how do we calculate what space is going to do?

QUOTE (Good Elf)
Recall that a single photon cannot produce standing waves by "bouncing around a cavity resonantly"


I will certainly remember that.

Best wishes - C2.


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