Problem with the two slit experiment, Observing later

Hi C2,

Let me suggest something to you. Expand your drawing 3x.
Take a drawing compass and draw 10 small concentric arcs expanding
inside each conic section radiating from each slit until they contact the screen.
When drawing the arcs, place the point of the compass needle on each corner of the slit output and draw the overlapping offset arcs. At the points of intersection at the screen draw a small circle around that intersection point and you will have your interference pattern with its phase shift induced by
the slits.

Regards,
LL

This post has been edited by Laserlight on Jan 3 2007, 07:49 PM

Off topic but of interest re: search for dark matter.

http://news.yahoo.com/s/space/20070103/sc_...rkmattervisible

Hello All,

Another off topic post:

I just read an article about astronomers finding a new black hole in a star cluster
50M light years from us.

http://news.yahoo.com/s/space/20070103/sc_...inunlikelyplace

I have often wondered if the reason that black holes don't radiate light is perhaps
because the intense gravitational fields that are present at the surface of the
dense core, located at the center of the black hole energy vortex, modifies
or prevents EM fields from forming a balanced energy EM wave "structure".

To further develop the idea, perhaps the gravitational energy is so compressive
that the normal atomic energy "gap" structure of the atom does not exist as we
know it and therefore electrons cannot jump energy levels to produce EM waves.

All of the concentrated electrical and magnetic energy that is available has
been concentrated to maintain the core's regenerative energy "dynamo".
The potential energy of the core's mass is concentrated as magnetic and
gravitational fields, while the kinetic energy component is maintained as the mass rotates on its axis. The event horizon is the energy point where normal
space ends and gravitationally warped space begins. It is the point where light,
travelling thru the vacuum of space, becomes diffracted due to the effects of gravity bending the path from the normal.

LL

Hi Laserlight,

Yes.. I may well have been making a point that refers only to one of the ways I have been attempting to analyse the DSE.

Looking at http://www.teachspin.com/instruments/two_s..._combiplot2.gif we can see that the centres of the slits are at about 5.8 and 6.5 on the scale. (I seem to remember calculating the separation to be 0.5mm but the calculation is near enough not to worry me). As far as the double slit interference is concerned the single slit outputs are virtually on top of each other and the single slit diffraction patterns turns into double slit interference when both slits are open. If the slits were further apart then (most of) the diffraction pattern would be the same except where the outputs of the slits overlaps. Point being :- the single slit condition runs smoothly into the double slit condition rather than replacing it. If we imagine deformed and drunken Russian soldiers dashing through the slits we see them forming a very organised pattern in the double slit interference region .. how would they manage to do that?

Diffraction/interference .. there doesn't sem to be much to choose between them except that the two slit interference is spectacular.

Best wishes,

-C2.

This post has been edited by Confused2 on Jan 3 2007, 11:54 PM

Hi C2,

Now that's funny! The Russian army is really in bad shape.

I don't think we are going to get "there" with your example. I suggest that
we leave the Russian army alone so that they can "recuperate" and get back
to EM wavefunctions. Soldiers represent "particles", not EM wavefronts that
exhibit interference.

Regards,
LL

What ridiculous pursuit?

Open PM to Laserlight.
I would be very grateful for your assistance to keep this thread roughly 'on topic'. It is bigger than any of us. If we cannot go forwards then we need to look back over what might have been missed.
Best wishes-C2.

C2-

IMO, the horse that we beat to death some weeks ago is now flayed to the bone,
and we are just rehashing past discussion points. I will now just become an
"observer" since, IMO, I have nothing "productive" to contribute to further
discussion on this topic.

Regards,
LL

This post has been edited by Laserlight on Jan 4 2007, 01:56 AM

Hi Confused2, Laserlight, Montec, TRoc, Jal, Duality, yquantum, Neil Farbstein et al,


The Rayleigh Criterion for uncorrelated sources...

This is nothing like what really happens. This may be where much of the misunderstanding is coming from... The "spread" depends on wavelength and slit width and separation and can be literally dozens of times larger in proportion to that "illustration" of the Airy Disks you have there.

The two "intensities" from the Fraunhofer Sources combine not as intensities but as correlated phased "arrays" and this is the whole point. There is no neat "overlap region" as you would get in the situation of uncorrelated sources and the Rayleigh Criterion where the first Airy minimum falls on the peak of the other source's central maximum. This would be the case for instance through a telescope where you are viewing two separated optical objects like two different stars separated by a small angular displacement, each one produces an Airy Disk but they do not correlate. While I can show you an Airy Disk I defy you to draw the interference pattern to the same scale on the same page for certain separations and slit width's for correlated sources.

This is not what happens... this is nothing like what happens... The "output" is nothing like "superimposing" the two Airy Disks because these are complex phases and they "mix" and spatially "beat" with themselves....
Wikipedia: Angular resolution - Rayleigh Criterion
This is for the Airy Disks of two separate sources that are NOT correlated and this...
Wikipedia: Phased array
... is for correlated sources.... This is the same theory as we have been discussing for Fraunhofer Diffraction with 'multiple slits". Read up there on it, sync pulses again as before.

Whatever the disputed cause... the "final resting place" of individual photons are the result of "photon one-on-one beam steering". This is why photons end up almost anywhere and not just "along the line of sight". I cannot predict "exactly" which photon goes where but it is the result of some intrinsic property such as the Berry Phase of the individual photon which you just can't "individually" measure.

Take one single photon in isolation and emit it from a very distant source (assuming we call this "travel", as you know I think this is not the photon itself that is moving in the vacuum). It "travels" to the screen through a series of nodes and anti-nodes already existing in the space (and defined by it) as if it was moving in a "cavity". After a period of time this tiny expanding wavelet (a single sync function, seeking all available paths, but complex in nature) arrives at the screen somewhere. There is a flash of light.

At a later time this same source now emits another "isolated" photon with exactly the same physical phase at source (t=0 φ=0) since all photons from this one atomic orbital emit photons with a "beginning" phase which is identical but a sufficiently long time from the first emission so it no longer correlates (the source is not being continuously "stimulated" to emit coherent radiation... in exact step). The photon could emit in any direction and the time of this emission is not related (correlated) with the previous emission's time as a frequency. The two emissions differ only in temporal phase not spatial phase ... they are "orphan lone emission lines". The progress "could" be identical to the first photon. Lets say the photon emits by chance into the same direction. Provided there has been no change in the geometry this second photon encounters the same nodes and anti-nodes on the way to the screen. It gets the same ride along the way and strikes the screen. There is a second flash of light. This photon will fall on the screen and be part of an interference pattern... but not the same pattern as the first photon. It will not "correlate" with the photons already there (just that first one at this stage) so there is no guarantee that it will "construct" the same pattern "with" the former photon. Remember the "construction" causes the photon pattern to be found over an extremely wide area in general. There will also be "sidebands" as well to these lone photons that are the result of the extra frequencies in a single photon packet. These extra frequencies cannot be on the same interference pattern as the other photons since they do not correlate and so fall on their own separate interference patterns which overlap the main interference patterns. The result will be "chromatic aberration" and individual line broadening. Not a big effect but a measurable one.

Next example... A hot incandescent lamp globe is covered with an interference filter which only allows photons of a single discrete frequency out since there are also band blocking filters above and below the interference frequency... one is a high frequency blocking filter and the other is a low frequency blocking filter so only photons of that one monochromatic frequency are able to escape. There are many being emitted but they are not correlated... some are heading toward the slit. They all have the same spatial source phase and frequency but they have different temporal phases (photons emitted at "irregular times". These will subsequently partially cohere "spontaneously" through free space Raman Scattering. This is like all your Russian Soldiers slightly changing step to form up along "spatial" lines rather than choosing to move chaotically. By the time they get to our first slit most have encountered the same nodes and anti-nodes as the first two photons but this time the space is resonating like a bell being repeatedly struck at a critical repetition rate of twice the frequency but each successive strike is opposite in phase to the previous strike which correlate to the "UP" phase followed by a "DOWN" phase. In the analogy of the Russian Soldiers ... first with the left foot then with the right foot etc... This "gaits" the photons spatially on their way to the slits. Unlike Russian Soldiers many of them can occupy the same temporal and spatial position on this "wave". No longer are these photons isolated lines with a wide band of temporal "jitter" being equal to or greater than a period of the base frequency but they now have refined their "timebase" so they form a single narrow line "resonant" at a single spatial and temporal frequency "lockstep" in time and in space. After the first few instants of propagation those sidebands "clean up" and we are dealing with almost "pure" single frequency light but composed essentially of individual complex sync pulses.

We can place a "neutral density (ND) filter" in the way of the first slit to block almost all of the coherent photons... Now there is only one a second passing the slit. What we find is these individual photons still fall on a single diffraction pattern "constructively" since the "timebase" still correlates even though a large number of temporal frequency intervals have passed since the previous photons have passed that ND Filter. The temporal frequency that correlates the source with the sinks on the screen has a repetition rate where the clock can be reset over and over.

Cheers

This post has been edited by Good Elf on Jan 4 2007, 08:56 AM

Hi Good Elf, Laserlight, Montec, TRoc, Jal, Duality, yquantum, Neil Farbstein et al,

Starting off with optics and waves..

Would it be possible (as a matter of convenience) to select possible diffraction effects from the menu shown here..

http://230nsc1.phy-astr.gsu.edu/hbase/phyo...ffracon.html#c1

It seems Fresnel Diffraction is simply a more detailed analysis of the effect known as Frauenhoffer Diffraction .. it isn't the effect that does or doesn't include a phase component .. it's the rigour of the chosen method of analysis.

I have no particular objection to the existence of Airy discs, the reference here ( http://support.svi.nl/wiki/AiryDisk ) suggests they are normally measured at the focal plane of the lens .. and we have no lens and no focal plane.

I suspect 'Fresnel Diffraction' (Physics) is the same as 'Airy Discs' (Optics). The reference here http://230nsc1.phy-astr.gsu.edu/hbase/phyopt/fresli.html#c1 includes a neat trick with the Cornu spiral which is explained in more detail here http://230nsc1.phy-astr.gsu.edu/hbase/phyopt/fresgeo.html#c2 ..

We can go into the calculation of the Cornu spiral if desired .. IMHO it already looks sufficiently evil to cover the requirements of a reasonably full analysis.
Sooo.. to me it looks like a Frauenhofer source is really a Fresnel source and a Fresnel source does include phase information.
I see no reason why two of these ( http://230nsc1.phy-astr.gsu.edu/hbase/phyopt/sinslit.html#c1 ) can not be sat next to each other (any distance apart) and as long as we proceed carefully we can get a good analysis without any problems, in particular the two slit result will appear without difficulty. It would simplify the analysis enormously if we consider each slit to have a width that is substantially less than a wavelength and would still give a good physical prediction. There is tedium but no magic in such an analysis.

As I work through your post .. up to this point there has been no consideration of anything other than continuous sinewave excitation... at this point there is no justification for claiming a sync pulse would give the same result and a great deal for claiming it wouldn't.

I see this too .. if we knew what steered a photon and how it was organised to steer through two paths of different lengths such that it gives the observed result I think we'd have the answer... not today, I fear.
Enough length and controversy for one post.. more will probably follow in the fullness of time.
Best wishes,
-C2.

Hi Confused2,

There are no two paths... the photon only travels on one path but it self interferes.

Wikipedia: Fresnel diffraction or near-field diffraction
... The "evanescent region".

Caption: The Fresnel zone is one of a (theoretically infinite) number of a concentric ellipsoids of revolution which define volumes in the radiation pattern of a (usually) circular aperture.
Wikipedia: Huygens-Fresnel principle
Wikipedia: Fraunhofer diffraction or far-field diffraction


A "bit from column A and a bit from column B" depending on the distance from "sources"... primary or secondary.

The sync function is the most simplest function possible to simulate an impulse of finite energy and duration.... that is it! Not only that it actually works!

Please note that this is a spatially distributed complex function and is represented by a complex plane 6 dimensional function (x,y,z,ix,iy,iz) in the real most general three dimensional case. In the same way I can't show you a Fourier Transform in a single snapshot either.

Cheers

This post has been edited by Good Elf on Jan 4 2007, 03:02 PM

Hi Good Elf,

You've nipped in again! .. I'll post before I lose this then read yours

Coherence and collimation

Let us imagine we have a laser source... we know (because we're told) that this is a reasonably good source of well collimated coherent monochromatic light. The beam from our laser is 1mm across and our slits are 2mm apart .. clearly we can't shine it on both slits at once. This would be an example of a photon that likes a particular path and has no interest in seeking other paths. How does such a photon differ from the more adventurous 'seeking all paths' type photon (or sync pulse if you insist?)

Tests..

1/ We use a half silvered mirror to slit the laser into two paths and create two beams and we shine one beam onto one slit and one onto the other slit. Quantumly divided coherent collimated beams? Interference Yes/No? (My guess is yes.. the pattern may be slighty shifted because using the two beams may introduce an effective path difference before the slits .. this will have the same effect as a path difference after the slit.. a maximum shift of half a wavelength )

2/ We shine the beam onto a translucent glass bead and use this as a source. Interference Yes/No? (My guess is that there will be interference 'in principle' but in practice the random path differences will make it statistically undetectable.)

3/ We shine the beam onto a narrow slit (as usual). This turns our coherent collimated beam into a coherent non-collimated beam .. exactly what we want. The slit would even turn a non-collimated non-coherent beam into a coherent beam.

In here is a nice account of photons from distant sources .. http://www.citebase.org/fulltext?format=ap...cl-th%2F0510049 No Raman scattering .. no lots of things .. just a bit of quantum.

Best wishes, -C2.

Hi Confused2,

I am getting tired of repeating myself and I am beginning to lose interest. Maybe I am beginning to black out from sheer repetition!!

Use a diverging lens then a collimating lens. This will give you a much wider "parallel" beam, this is implicit in all of this discussion. Otherwise just step back a couple of hundred meters you will find that the beam will still spread eventually. Of course there are "always" sidelobes to the radiation pattern of every source so there is always that effect regardless of collimation or divergence (just considerably weaker). What do you want to know... Fraunhofer Diffraction or Double Slit Interference??? Illuminating a single slit or small circular aperature is just applying a "spatial filter" to the beam. You know what the results are for each. Just remember that a pinhole is a very small optical lens of any nominated focal length except you have applied a very "tight" spatial filter to it.... that is all.

This fact can be used by people with gross deficient optical ability to enable them to see in bright light tightly focussed images of everything up close to infinity with nearly infinite depth of field. A pair of cardboard glasses with one pinhole at the center of each cardboard eyepiece works as well as $100 set of optical frames and lenses in the bright sunlight for "everyone" and for all focal problems.

You must illuminate both slits evenly for really successful double slit interference. Please exercise some "common sense" with your questions. You really need to find out for yourself and therefore you need to read up on some stuff. I do my homework so you should do yours as well so that you ask "non-trivial" questions. The Hanbury-Brown-Twiss Results have no bearing on this thread and though it had some relevance to coherence length we are not doing stellar interferometry here... we are dealing with Young's Double Slit Experiment. I just would like to say I have probably said enough on this thread for any reasonable person to connect up the dots without my writing some kind of Tertiary Textbook. I have provided all the necessary cross-references you need to find out everything you have requested (several times over).

Cheers

This post has been edited by Good Elf on Jan 4 2007, 03:46 PM

Hi Confused2, Laserlight, Montec, TRoc, Jal, Duality, yquantum, Neil Farbstein et al,

I am sorry that I got a little "tetchy" last time but I was a little overtired. We are going in circles and it is difficult to see if we are making any progress at all. I think all we will ever be able to do is supply an alternative to a pure quantum approach as long as the model is confined to three spatial dimensions. It is my contention that there is an indeterminacy in the system which can never be resolved simply due to the process of measurement. Quantum Mechanics makes no attempt to resolve it and "semi-classical" approaches can only show that these photons are simply "consistent" with individual destinies without being able to determine them.

It is a historical fact that Quantum Mechanics "chose" this path at a time when resonance was not considered a primary motivation in explaining outcomes. Since all resonances lead to statistically insignificant outcomes because over time a resonance averages out to a simple "lower density" due to the effect of "frequency", it was probably ignored.
+ =
This is the time dependent part of cavity resonance for an S orbital.

A single proton will produce this cavity resonance anywhere in space... where ever you put it. The proton is not apparently a completely primitive object and is composed of three fractionally charged "quarks" which have different influences on each other and cannot be separated any great distances from each other before the energy of that separation is sufficient to create a new "quark system". The fractional charges and the large masses of the individual quarks are not strictly scalers as we consider charge and mass in the real world. What I mean is all particle theories must bend over backwards to make this all work. Quantum Mechanics offers no mechanism for this other than saying that it just happens.

The 6 quarks and their most likely decay modes. Mass decreases moving from right to left. (Shown are quarks .... there are also anti-quarks)

There are large numbers of other "resonances" and there are two conventional ways to interpret the menagerie of entities... one is the "particle" the other is the "excited state" both "explanations" decay in the time light takes to cross them. If you accept that the "excited state" is the explanation then the answer lies in a unified electromagnetic theory where the individual states we term particles are analogous to the excited states in "optical cavities" in QED. This can lead to a novel interpretation of "supersymmetry".

This "second interpretation" of "particles" as "resonances" hardly ever occurs in the literature. It "explains" such things as the mass oscellations in neutrinoes and the way mass is shown to be the result of the "strong interaction" above in the illustration where lower more stable configurations of the "particles" lead to lower masses through "resonance decay". Notice also how there is an indirect relationship between "charge" and "mass".

Once again I apologize for my loss of patience. Lets all try and break new ground not wear a circular patch on it by going in around in circles.

Cheers

Good Elf,
Tetchy? My fault entirely, sorry, too caught up in the topic. I will take a break from it.
Best wishes, -C2.