Problem with the two slit experiment, Observing later

Guest Confused2.

This should help.

http://www.optica.tn.tudelft.nl/education/photons.asp


LL

Hey C2, LL, TRoc, GE, et al.

Troc, I think you airplane analogy was one of the best that I've heard (it also can be "morphed" to describe group and phase velocities). But I think it justifies (and does a great job of explaining) the necessity of the "all paths" model in single photon DSE. When traveling "one passenger at a time", there is no way to know who is sitting where, including the pilot's seat; so all the passengers sit in all of the seats during the flight.

C2 - maybe this link will help. http://cns-alumni.bu.edu/~slehar/fourier/fourier.html Particularly the "spatial frequency" and higher harmonics. Defraction, defraction, defraction........

Hi Laserlight,

Remember what is true about "optics" is also true about Radio Frequency Engineering. It really only differs in the scale. Now in the DSE the electric fields do not go down one path and magnetic fields go down another... Electromagnetic Fields are "Complex" in nature... that is not in the Real but mathematically Complex (involving the square root of minus 1)... It is not necessary to argue about the nature of the photon... it is known and experimentally demonstrable that photons can only self interfere because they are bosons. How and why they can pass through two slits at the same time is not in dispute, this is experimentally verifiable, if you do not believe me cover one slit. This is a difficult philosophical concept for those tied exclusively to quantum particle theories.

C2, diffraction is not used to "separate frequencies" that is "dispersion". Diffraction is a single slit, one frequency at a time phenomenon similar to interference where you have two slits. In fact interference is the superposition of two diffraction patterns.

Cheers

Basic Double Slit

Description
http://www.colorado.edu/physics/2000/applets/twoslitsa.html
Calculation of result
http://schools.matter.org.uk/Content/Inter...ce/formula.html

-C2.

Edit .. LL, this is where we should have started .. sorry.

This post has been edited by Confused2 on Nov 7 2006, 01:20 PM

Hi Confused2,

I suppose you realize the formula is wrong since they do not account for the variation in slit width. The "simplified" calculation shows no variation for slit width and neglects the Fraunhofer Theory. I have even seen this formula being substituted for a "Gaussian Function" (I think misleadingly) usually used in Quantum Mechanics, yet simple experiment will show this function below is indeed more correct. If you make the individual slits broad enough you get a soft blur for each slit, that is what your illustration shows. Narrow the slit width further and there is a much finer single slit (Fraunhofer) pattern there. This pattern is the same as if you use small slit width and large separation between the slits in Young's double slit "interference" experiment... You would obtain two separate patterns... allow the slit distances to reduce till the patterns overlap and "bingo"!

This is the "true" more complicated formula for one slit or more than one...
Three Experiments in One
Here is the "envelope" for a single slit...

And this is the pattern for a "pinhole".

You get the "slit" from a continuous series of pinholes. Notice the much smaller but still existent secondary peaks. Two of these patterns separated by the appropriate interslit distance you have in your formula will reproduce a double slit pattern if added phase for phase the desired result. Notice this is a Fourier result as shown in the reference.

Half way down the reference you can see that the sum of n slits of width b and separation h is more of less given by that formula...

For some unknown reason the Web has a true paucity of information on this basic physics and considering just how important this is to the double slit experiment I think it could only be due to "ethnic" differences The double slit interference experiment cannot be understood without an understanding of single slit diffraction... it involves those Bessel Functions again... see below in the reference above.

Cheers

Hi Good Elf,
I think the formula I suggested is good enough to help us establish the principle. Bear in mind that we do not seem to have agreement that an EM wave can even pass through a slit ..
'Diffraction' is the reason why the light doesn't just carry on in a straight line ( if we accept that it can actually pass through the slit in the first place).
Here is a nice applet
http://micro.magnet.fsu.edu/primer/java/di...tion/index.html
No cavities and no resonances where none shown.
A reference to help us to calculate the intensity when the slit is less than a wavelength wide would be nice .. I'll keep looking, would you be kind enough to post or PM me if you find one?
-C2.

To me it looks like the 'Three experiments in one' just bung in a constant © and ignore the total intensity.

From..
http://www.physicsforums.com/showthread.php?t=139512

This looks 'true' to me .. as long as we keep our slit <= a wavelength then all minima in a DSE must come from interference. Absolute intensity as a function of input intensity and slit width remains to be found.


This post has been edited by Confused2 on Nov 7 2006, 07:10 PM

Troc, (anyone?)

The results of the formula here..
http://schools.matter.org.uk/Content/Inter...ce/formula.html
taken with the formula for diffraction here..
http://micro.magnet.fsu.edu/primer/java/di...tion/index.html

have (for the last hundred years) given a satisfactory prediction of the results seen in the DSE. I draw attention to the fact that neither involve any assumptions about frequency except that it is the same as that of the source and that it is the same at all points throughout the DSE.

I invite you to present your prediction..

-C2.

Confused2, Good Elf, TRoc, and all,

C2- Isn't the single slit experiment that you refererenced verifing, that in fact,
light does generate interference patterns going thru a single slit when the
slit is smaller than the wavelenth of the incident light? In order for interference
to occur there has to be phasing interaction due to diffraction delays of the light
which is a harmonic phasing interaction. IMO if there were 2 properly spaced slits
with separate incident beams that the interference pattern generated would yield
results identical to the standard DSE as wave fronts
overlap, thereby harmonically creating constructive and destructive interference patterns.

Another issue that I have concern with is the wave interaction of the
incident light beam reflections from the opening of the smaller slit. That energy
is reflected back toward the light source and should create some interference
in the incident beam.

Read my first post on Nov 1.

Do you agree or disagree?

LL

This post has been edited by Laserlight on Nov 7 2006, 09:00 PM

Hi Laserlight,
I'm not trying to be evasive ..
This applet doesn't allow you to make the aperture smaller than the wavelength...
http://micro.magnet.fsu.edu/primer/java/di...tion/index.html
For any width of slit I would agree that interference occurs (though not always total) .. to eliminate it completely we would have to make the slit infinitely narrow .. which is useless because it would give us an infinitely low intensity to work with.

I'm with you up to the point of "harmonic phasing interaction" at which point I don't understand what you mean. Could you clarify that a bit please? So far I only see "fundamental phasing interaction" because we started off with one frequency and we have no non-linear elements.
The next bit looks like it might be beyond my imagined level of competence .. can we sort out the 'harmonic' bit and see what drops out?

--------------------------------------
Going back to your first post of Nov 1st .. (if you click on Posted: you can cut and paste the URL )
http://forum.physorg.com/index.php?showtop...ndpost&p=139249
The 'main problem' with what you suggest would seem to me to be that interference takes the same form even when there is only one photon present. I know of no difference between the result for a lot of photons regardless of whether they come individually or all at once.

The DSE has been performed so many times and so carefully and in so many ways that I don't think bounces and scatters are adequate to explain why the result is always in good agreement with the equations given previously.

Looking at http://www.optica.tn.tudelft.nl/education/photons.asp .. do we not both see well defined maxima and minima? Do you find fault with the experiment? I can find others if you wish.

-C2.

All, please feel free to contribute (on either side).

Hi Confused2, and Laserlight et al,

I think we are working at crossed purposes here, the reason that double slit diffraction works is simply because of single slit diffraction based on Euler's relationships in the complex plane... It is not because of the explanation you are giving. This is also why RF propagation and a host of resonant phenomena also work, one principle for all instead of a host of "dumbed down" formula, one for each circumstance. With all due respect your suggestion that near enough is good enough when we are speaking of real phenomena just does not wash. I am not talking about something beyond the realm of observation... in fact this was one of the first experiments I was actually able to see with my own eyes. This "principle" can be tested with a monochromatic light source and a small laser punched hole in a gold foil (a perfect "pinhole"). The example illustrated/cited was a little "skeptical" simply because human engineering has not reached this level of accuracy to be able to make grids this accurate over such large spatial areas yet (I really mean "large" spatial areas since the effect spreads throughout a pretty big visible distance). However to keep on track with the DSE it is much simpler to just use the first two terms in the equation shown and that is a two slit diffraction pattern... you supply the slit widths and inter-slit differences. This general "construction" works with any nominated spatial pattern over any surfaces since any "hole" or "slit" or complex combination can be constructed from a series of "pinholes" (that is something like how Feynman's construction works only it is using a quantum paradigm). Of course computers do these things in a "doddle". Therefore "approximate" distances between slits and slit widths large enough to be measured in a school lab give "pretty good results resulting in an intensity map across the plane. Your formula only supplies a "single line series" of zero width, where the center of the dark bands and the light bans occur, it is an ad-hoc "connect the dots" point of view. The error is that formula does not predict anything about the intensity at any peak or in between (or phase). This is not telling us much about the variation in radiation pattern, the actual numerical variation in "brightness" across the field of observation (eg. Dipole antenna, diffraction of light near an edge or in the more extreme case but not essentially different one of the radiation patterns produced in atomic orbital "cavities" etc.).
Spherical Harmonics of the Hydrogen Atom
This Java applet shows how the Bessel Functions "evolve" on the surface of a sphere through spherical harmonics and produce all the quantum numbers which are just the eigen states of "shells". You have the ability to do inner products or not and fiddle with all the possible combinations of quantum numbers. The classical result differs from the quantum approach not in value, but only in the nature of the quantization process (the fate of the "eye of the hurricane")... tiny single flashes of light (individual photons) and to their statistical positional evaluation (inner product population distribution over time). The real or complex numerical values of the gradation between the light and dark areas can be determined from this fuller optical approach exactly (equation given) and you really do not need to think about it any further... the diffuse light and dark regions and their exact intensity relationships spatially can only be explained by this "fuller construction" through squaring the projection of the phasor (inner product projection) on to the screen plane. This process can be extended to three (...or even more?) dimensions. Solve it once and then hand it over to a computer to do the slog work. Elves do not like calculations eh!

Cheers

This post has been edited by Good Elf on Nov 7 2006, 11:26 PM

Hi everyone,


I think we are making progress. I will address C2’s question of “where do the other frequencies come from?”


GE has explained several times about the spread out nature of the wave packet. This is the fundamental nature of a waveform, and the fundamental nature of frequency is that it is the rate of cycles over time. If the waveform spreads out over time (change in distance), then it can only be represented by frequencies that encompass that time. But we don’t have to limit the explanation to “ideas”; we have an abundance of empirical data.

Planck derived “h” from using Boltzmann's’s statistical version of the second law, based on probabilities. He didn’t like that, but it worked. (Einstein didn’t like it either, but was able to explain the photoelectric effect with it.) These 2 theories are critical to QM, and they show the underlying mathematical procedure that is essential to making sense of the “large number” experiments. The one thing that is certain: these mathematical procedures are designed for MANY, MANY photons. We do not need statistical analysis to determine the interactions of VERY small numbers of things (1,2,3, etc), it is a mistake to do so.

We also do not need to measure complex sine waves, or angles, although they arrive at the same conclusion. I will vote for the easiest way every time.

I’ll start with the link that GE gave us.

Any part of the slit can be thought of as a secondary forward traveling spherical wavefront, the coherent superposition (with the original signal) of which produces the diffraction pattern.

You’ll note here that the creation of the wavelets (beat frequencies) and there subsequent summation, is CRITICAL to this explanation. You will also note that the Fourier transform can be used here, but the reason that I question its’ usefulness here is that it just “..gives us a relationship describing the slit itself.”
This process (as you noted) is critical to my theory as well. You just need to remove the Fraunhofer Plane (we don’t have a lens after the slit) and replace it with an “interaction zone”, where my beats can sum. This is a “quantum Hubble distance”: a limit, controlled by the constant speed of light, that regulates how many cycles can interact in a given time, or distance. Our signal, of course, is “just passing through”, and there is just enough time for a “handshake”, and the “new pilot” is hired.

I can not say that any better!



A little on filters:

As I have said, the laser output is not strictly monochromatic.  This is addressed through filtering, however, a quick look at the output past the filter will tell you that it is still not monochromatic.  Here is a chart from the output of a 543.5 nm filter.  Semrock




543.5 nm


You’ll note that it looks pretty good this way, but the peak signal is not 100% of the transmission.  Where is the rest of the energy?  E=hf still works, but you have to calculate new frequencies, and sum them together for energy to be “conserved”.  Here is a small portion of the list of frequencies that is “measurable” at the output of the filter: (only >1/1000 occurring frequencies, the actual list goes from 470.8 to 720nm in .2 increments, and shows >0 at every value!)

541.4 0.001098408
541.6 0.002422708
541.8 0.005807638
542 0.01537755
542.2 0.045588677
542.4 0.148528815
542.6 0.448993228
542.8 0.846683103
543 0.98614677
543.2 0.998722014
543.4 0.998125327
543.6 0.998233365
543.8 0.999009228
544 0.986664727
544.2 0.850802654
544.4 0.460517668
544.6 0.156462124
544.8 0.04900649
545 0.016801658
545.2 0.006439494
545.4 0.002724325
545.6 0.001252253


So, the reality is that there are already many frequencies present.  The REAL question is what is happening to the energy?  Certainly, a purely additive approach will not work.. the UV catastrophe would happen!  Just the handful of frequencies that I listed would be many orders of energy than we know (measure) to be present.  Last year, I showed you and GE my approach to the black-body spectrum.  A linear “beat frequency cascade” that exactly matches A. the change in energy, graphed out in a curve that is not reproducible by “classical” means, and B. the discreet, incremental frequencies observed as the “body” changes colors, and even going further, to explain the “mysterious” absence of green in the spectrum of a heated BB.  That, of course, is another post, but I want to make the point here that the discreet “sum and difference” method can be more simple than the “infinitely divisible” approach, and still be predictive.  Here is a paper making a similar statement:

Quantumlike Diffusion over Discrete Sets 


Also at that time, I told you both that I had a method, and equation for deriving the Triad/chord in music.  This is no trivial matter.  The step by step method gives an explanation not achievable by the complex statistical analysis.  It predicts the results of the current rules for “four-wave mixing”.  So, when I gave you the equations, those were “from the book”, not my version alone.  I dug up the paper that I referenced (EM version of the mixing), and found the on-line link for you.  This is THE BEST paper, or single source for FWM that I have found.

Four-Wave Mixing and its Applications

The only “stretch” that I ask (and it’s not much of one, IMO) is that you consider the input (laser) as “one” frequency, and the divided path of the 2 slits, as “two” frequencies.  This is directly suggested in the beginning of this post, as well as inferred in the links I’ve provided.


Parametric Self-Oscillation via Resonantly Enhanced Multiwave Mixing

Nonlinear optics via double dark resonances

In case you missed them the first time around, I have offered links to suggest the existence of the “quasi-cavity”. Several of the papers say specifically, that “no cavity is needed”, when describing their particular interferometric experiment. I will add here that the Casimir effect works because of the “approximation” of a cavity by two parallel planes. Certainly, the slit “wall”, and the screen fit that approximation. (as does the “wall” of the enclosure behind the laser, and the slit wall)

Also, you might browse through some Wikipedia articles:

Optical parametric oscillator

Nonlinear optics


Harmonic mean

We must be careful when translating Pythagorean harmonic ratios into average rates and discreet quanta. Plancks constant makes all the "bits" the same size. My method preserves ratios through a scaled harmonic mean; which is fundamental in comparing things to the constant ratio of the speed of light. This is why h fails to communicate the harmonic nature of the scale of the Universe, also the home of the c ratio.



ciao!

T.Roc



This post has been edited by TRoc on Nov 8 2006, 12:24 AM

Hi C2,

I definitely stated that wrong, it is the beamwidth that is wider than the slit.
My Bad....

I guess my point of contention, and the reasons for my consternation, is the way the interpretation of the results of the
DSE are explained without regard or consideration of the physical interactions
that occur when light interacts with matter. Both have EM "fields", and when EM
fields are sufficiently close or intermingle they cause mutual interactions between
the two distinct EM energy entities. The results being either reflection, refraction,
scattering, phase shifting, or absorption of the EM fields of the photons. Since the individual photons can travel down the center of the slit with minimal EM field
interaction, or can traverse in close proximity to either side of the slit where there
is high probability of refraction and phase delays between photons, there is
room for doubt or further understanding of the implied results

My second issue has to do with the backscattering of photons toward the
incident beam. That should also set up reflection standing waves, which could
cause a variable phase (destructive interference) phasing mismatch of the incident
beam before it even arrives at the slits. If this does in fact occur, what is the
consequence on the results of the experiment? Also, is there any cavity resonance
of the photons reflected back from the reflective plane of the slit housing within
the confines of the beam width? Does this generate secondary effects?

My thiird issue is the dual reflective plane surfaces of the mirrors that inherently
creates a phase and timing delay shift of photons due to refraction interaction thru
a media where some photons travel thru the glass at an offset angle from the inicident beam before finally reflecting toward the slits.

None of these issues seems to be considered in the conclusions reached by the
experiment. Maybe they don't need to be, but perhaps they do.

The equations back up the theories, and I cannot refute that, but are we really
understanding all of the factors that influence the end results, and are the
assumptions and all potential variables accurately articulated to insure complete
understanding of the phenomenon.

Sorry if I am beating a dead horse, but I have more questions than answers.

LL

This post has been edited by Laserlight on Nov 8 2006, 12:41 AM

Hi Confused2, Laserlight, and TRoc et al,

I really do not want to involve myself in any difficult discussions about what may be the most expedient method of processing a very simple problem. What I am saying is this method I am outlining is the full method of processing that will work anywhere. An implementation of this showing Feynman Calculations, disclosing documentation of the methods and the original reference back to Feynman's original book on the subject...
Good Elf on Feynman earlier in this thread
QED: The Strange Theory of Light and Matter. (Alix G. Mautner Memorial Lectures) Richard Phillips Feynman
Now Feynman's treatment is very good but I do not think this is in anyway "inferior" at the level of a calculation to this purely "Classical" view of the phenomenon. There is a section in Feynman's Lectures in Physics Vol 3 as well that covers this in greater details. What this treatment does not handle is a particle description of the phenomenon. Let me say that as long as the photon is in free flight, only the wave description could ever be applicable since it has calculable "solutions " throughout all space whereas the particle approach cannot solve for anything but uncollapsed states (now we have a "measurement problem" that is introduced through the very act of measurement. Of course once you collapse a superposition of states for the photon "particle" it is no longer treatable as a pure wave propagating from a source. Qubit all gone! The "beauty" of the wholly wave approach is you now can calculate values for the wave throughout the entire Universe except when it has been "collapsed. "That is still a pretty good solution!" as Feynman might have said in his heavy Bronx accent.

What it will not predict is the "eye of the Hurricane"... center of spin which we all identify as the heart of the photon. What it does say is that for large numbers of photons the "complex vector's inner product squared" is a measure of "brightness", this is clearly an electromagnetic energy density (it is often visible light... it is the RMS value of the instantaneous Electric and Magnetic fields). While the wave of a single photon lies on a "search all paths" ever expanding shell (with its internal clock stopped), this photon will collapse to a single flash of light at its "center" by the process of transverse wavefront "locality" which is an infinite speed (phase velocity along the wavefront). This you can equate with psi squared for an infinitesimal dv. To determine the probability if a nominated photon will be "found" within a certain finite volume of space just add up all these psi squared values for all the dv's in the finite volume of interest. This will give a probability (when normalized) from 0 to 1. That number tells you what is the chance that a flash will occur in that volume of space and not outside that region. Bingo ... quantum theory.

Cheers

Good Elf, EXCELLENT! Now to expand upon your "eye of the hurricane" analogy a
bit further. Does a single drop of rain a hurricane make? Of course not,
but trillions of drops rotating along a wavefront and moving along a vector do.

I think we agree that indeed waves are easier to comprehend, predict, and measure
theoretically and mathematically because photons "en masse" are consistent and
predictable in how they interact as one "unit" and with matter in time and space.
After all, isn't a wave just a multitude of individual nearly synchronous energy packets
with infinitesimal angular displacements of location and phasing over a time
interval. In other words the composition of a wave is comprised of the interactve
angular phase timing delays of the discrete EM fields of individual photons over
a distance, along a time vector.

So a wave, as such, is dependent upon the phase timing interaction of discrete photons of which it is comprised.

Comments welcome by all.
LL

This post has been edited by Laserlight on Nov 8 2006, 05:12 AM