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> Problem with the two slit experiment, Observing later
Duality
  Posted: Dec 20 2006, 12:36 AM


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TRoc, LL, jal, Confused2, yq - [stepping out of the box for a few], Good Elf, all,

Before I descend down into the archives I wanted to share this with you all.

The mathematical theory of quantum mechanics is now 75 years old and continues to describe a huge variety of empirical observations with great precision and without anomaly.

No controversies exist about its basic validity. On the other hand, no consensus has developed on how quantum mechanics should be interpreted metaphysically.

The Copenhagen interpretation of quantum mechanics, promulgated by Niels Bohr in the 1930s and largely accepted as convention until recent years, says nothing about consciousness.

However, it left the door open to misinterpretation with its positivist insistence that only what is measured can have any meaning. As is often heard in physics classrooms, "the electron has no position until that position is measured."

Technically, this just means that we cannot include the electron's position in any theoretical equation until that position is measured. However, this unfortunate wording has led some to the logically fallacious inference that the electron does not exist as a real, localized particle until the performance of a conscious act of measurement.

Alternative interpretations of quantum mechanics have been proposed over the last several decades so you guys are on the same journey.

The trouble is no one leaves much space for consciousness, however some open the door for further ideas and where they might come from, my suspicions is from the most unlikely places.
You never know, but use fundamental laws to support your ideas, or you will fall into the trap we all have one time or the other in our careers.

Duality/Lisa


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Confused2
Posted: Dec 20 2006, 12:42 AM


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D/L,

I've had this old box for over thirty years .. any help to get it open would be greatly appreciated..

Best wishes,

-C2.

TRoc, GE, jal, LL et al .. I can't make any progress without you .. it would be empty. I hope that is at least understandable.

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Confused2
Posted: Dec 20 2006, 01:10 AM


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LL..with good nature you do not ask a second time for comments...

1. Energy cavities ..??? No storage properties previously known or described.. more detail please.

2. As 1.

3. See ripple tank (same mathematics) .. both slits are in phase

4. Harmonic oscillations .. same frequency as source? Delay .. energy ADDED .. ??

5. Randomisation .. ok.

6. 'Projection' .. sounds like both slits must cooperate or photons would just get lost completely ???

7. see 3.

8. see 3?

9. see 6.

The ball is returned.

Best wishes,

-C2.
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TRoc
Posted: Dec 20 2006, 01:42 AM


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Hi all,


Ditto on you being totally welcome here, Lisa.

Don't ever take offense to any critique I make of the problems in QM.


In case you missed this statement before, I and everyone here, will all agree that the "correctness" of QM or S/GR can not be argued against.

Just some "refinements" to models and definitions. But we all agree that any "final answer" one of us may come up with MUST match the empirical data.



LL has inspired me for a "binary" explanation for what I am trying to say. That way, "colors" wont get in the way.


The last link, provided by Lisa, and commented on by Jal: the piano, and the octave of light. I have said before, and it's a good time to say again, that SEVEN parts, with EIGHT steps did NOT work good enough. Music was ALLOWED to progress into the "classical" era through discreet quantization. (rather ironic use of words)

12 parts works MUCH better, because of the symmetry it provides. Prior to the 12 root of 2 to define the steps, they were UNEQUAL. Very hard to work with.

12 parts gives a "top and bottom", that are NEUTRALS (green and magenta), and 5 parts for each side of the circle.

You can see the problem, even in the "out of the box" example of the piano, with 7 keys from RED to VIOLET. We all know that Red is NOT the "same" as Violet, and green is in the center of the visible spectrum. So, in that example, you see that green is NOT in the center. In terms of what we can see, UV and IR are the same: "dark". They are the full octave, and the 1:2 ratio.


So, for LL's binary explanation, let me set the parameters.

R__Y = 1,0
V__C = 1,0

When you have 1...1 (R__V) you get a dark band,
when you have 0...0 (C__V) you get a light band.

For the narrower slit
When you have 1,1 (R+V) you get magenta (however, this is impossible from the frame of reference of the screen)
when you have 0,0 (C+Y) you get green

So, 1,0,0,1 is the "normal" spectrum (R-G-V), and

0,1,1,0 is the inverse. (Y-M-C) The inverse only happens with multiple images on the screen, like this

1,0,0,1,1,0,0,1,1,0,0,1 (light/dark/light/dark, etc) for BOTH SSE & DSE

When you block one slit in the DSE, you "squeeze" the pattern to this

1,0,0,1 which is an additive triad, and sums to white light



regards,

T.Roc



This post has been edited by TRoc on Dec 20 2006, 01:46 AM


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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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Duality
  Posted: Dec 20 2006, 02:08 AM


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Everyone should love this paper, I think?

I am going to take a break now, but I think I found you something down at the bottom of the pile, you might enjoy reading this paper and it is free and updated.

http://www.citebase.org/fulltext?format=ap...nt-ph%2F0506199

Be careful not to jump into a false security, but YOU ARE NOT ALONE. laugh.gif

Bonus it is going to give both sides of the problem of measurement due to QM personality's. laugh.gif

Duality/Lisa

Must get some sleep, it has been a very busy day! blink.gif

BTW, check into the GRW theory!
This you would have to pay for but you can at least read the abstract.

http://adsabs.harvard.edu/abs/1996PhDT........34L wink.gif

This post has been edited by Duality on Dec 20 2006, 02:14 AM


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Laserlight
Posted: Dec 20 2006, 03:10 AM


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C2,
I am authoring the answers to your questions and will post them when
done.

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LL
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Laserlight
Posted: Dec 20 2006, 05:06 AM


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C2 and All,

Thanks for raising the questions about my DSE model. I will
endeavor to answer them clearly and simply.

QUOTE
1. Energy cavities ..??? No storage properties previously known or described.. more detail please.


1. Slits being energy cavities:

The geometry of the slits are cavities with an
atomic vibrational"energy signature" all of their own. All matter
"radiates" vibrational energy due to atomic movement of its
micro structure. This is its EM energy signature. This is
how we can visually discern different materials by how they reflect
light from their surface. Each material vibrates at a different
frequency and light reflects from each "surface" differently.

Since the slits have close order geometric surfaces (edges) they
are coupling their vibrating radiating energy EM fields into
the cavity area.

Typically, sharp edges, because they have a 270 degree exposure area,
are high density energy areas relative to a normal 180 degree
flat surface plane. (I know this from working with sub-micron
scale geometries in the semiconductor manufacturing industry.)
A thin wall then, has two each 270 degree exposure surfaces (=540 degrees
per corner) radiating energy into the immediate area of the cavity. That is
50% more exposure surface area that is radiating/vibrating energy
than would be coming from two 180 degree flat planar surfaces from
a single wall. Now consider that we have 4 sides (8 corners) to the slit, that is
around 200% more available vibrational energy than 2 flat wall
surfaces radiate for the same area density.

External energy entering each "energy cavity" increases/changes
the natural vibrating "ambient" energy of the cavities. I
think this is where TRoc's harmonics come into play. The
cavity "rings" with the addition of external energy above
its normal ambient level. This is where the instantaneous photon phase angle
adds its energy component, which is the instantaneous energy applied to
the "cavity". When photon energy comes into phase with atomic
vibrational energy, energy transfer/modification should occur.

QUOTE
2. As 1.


2. Oscillations of the cavities "resonating".

The EM fields of the arriving photons inductively couple to the fields of the
cavities, and resonance takes place. The intensity of the resonance
is directly proportional to the phase amplitude of the EM wave as it
enters the cavity fields. The instantaneous amplitude of the arriving
photon's EM field adds a specific amount of energy to the ambient
fields. This energy coupling is a electrical transformer on an atomic
scale. When energy harmonically couples between fields, there is a
phase timing delay. Photon EM energy is coupled to the energy
of the cavities and is then coupled/reflected back into the energy
of the passing photon, but its phase timing has been shifted, The
slight phase mismatch changes the energy of the photon's fields,
its momentum, and its trajectory.

Once clear of the slit EM fields, the photon's EM fields reestablish
symmetry and the photon travels on its new deviated trajectory path
to the screen.

QUOTE
3. See ripple tank (same mathematics) .. both slits are in phase



3. Signal clipping of the photon's energy fields has to do with its
proximity to the sidewalls (and top and bottom) of the cavity and
its phase relationship at that instantaneous point in time.
Since the arriving photons can either travel down the center of
the cavity, or very close to any cavity wall, its waveform EM fields that
are in closest proximity to the nearest wall will be distorted by
the interaction of the fields of the cavity. This is where the biggest
influence on flight path deflection takes place, IMO.

Keep in mind that the EM waveform can be in the positive or negative 1/2
of the EM wave cycle. This is the "instantaneous uncertainty" of exactly
where, and at what energy point, the angular phase rotation the EM field
is at as it enters the cavity. Depending upon which 1/2 of the wave the
photon is in will determine which side of the screen "centerline" it will
deflect toward.

In all cases, the resultant screen waveform centerline splits the physical
center of the slit geometries.

IMO, this proves the phase matching aspect of the resonance of the cavities
with the rotational phase of the photons. There is balance/symmetry
on both sides of the resultant screen waveform.

As the phase delayed and distorted EM fields reestablish waveform symmetry,
upon departing the cavities, the photon continues along its new directional
path to the screen.

QUOTE
4. Harmonic oscillations .. same frequency as source? Delay .. energy ADDED .. ??


4. Answered in 1 and 2 above.

QUOTE
5. Randomisation .. ok.


5. Ok

QUOTE
6. 'Projection' .. sounds like both slits must cooperate or photons would just get lost completely ???



6. Each slit is its own harmonic vibrating cavity. There could be some energy
cross coupling to departing photons if they are within the vibrating
proximity of the EM fields. The physical symmetrical geometry of the slits,
plus the fixed geometry of the gap spacing, and the variable geometry of
the arriving photons comprise the relationship of the formula that you posted
previously. The formula works to describe the result of the geometrical
relationships.

QUOTE
7. see 3.


7. See answer to item 3 above.

QUOTE
8. see 3?


8.  See answer in items 2 and 3 above.

QUOTE
9. see 6.


9. See details about wave symmetry in 3 above.

cool.gif

Comments, discussion, disagreement, questions welcomed.

LL

This post has been edited by Laserlight on Dec 20 2006, 05:20 AM
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Good Elf
Posted: Dec 20 2006, 06:55 AM


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Hi Duality, Laserlight, Confused2, TRoc, Jal et al,

I have not left work yet so I would like to start the discussion but not finish it yet. I note with agreement that there is nothing wrong with Quantum Mechanics as far as it goes. What I think some of us want to say (at least me) is that it is a "three dimensions plus time" theory of quantum processes. It was never designed to describe higher dimensions... never ever and cannot proceed without a lot of revision beyond that "box" that is designed into it right from the start. The Universe that Quantum Mechanics has no limit to the space it exists inside and that is the source of a fundamental problem since we have identified that there is a real phenomena that is related to 'limited available dimensional space".

Now consider the dual slit experiment with the slit itself as a "source" as noted by Laserlight. There is absolutely no point in discussing "resonant cavities" near that slit when we are dealing with an almost ideal Einsteinian flatspace... Do you see that you are trying to use "higher dimensional" lingo while still trying to describe everything as if it was on the flat. Atoms cannot reside in real cavities, open space does not resonate as if in a cavity simply because it is not confined to a higher dimensional cavity unless space itself has higher dimensions. That is why Confused2's ripple tank continues to have "propagating or traveling" waves which are non-physical and can be shown to be that way with the Delayed Choice Quantum Eraser Experiment.

You just cannot have standing waves in places where there are no cavities. This includes the dark space where we have placed the screen. Resonance and interferences leading to standing waves just cannot occur in the dimensional box of choice ... three dimensional flatspace plus time. There are no vast gravity fields here to distort spacetime into the requisite closed higher geometry. That is fantasy and you can forget it... this is not standard theory it is a "Quantum Theory" with all its attendant "postulates". Lets admit it... you have already made unsubstantiated postulates (like it or not) when Quantum Mechanics says "lets have stationary states". That is not physics it is a "cold assumption based on nothing more than a need to justify the analysis".

None of us can afford the luxury to be so slack in our analysis to mix our metaphors and use this "doublespeak". If you want to use the language of Spacetime and Quantum Physics you are forbidden to use higher dimensions (above 4) to describe these "cavities". I can show you the cavities so we have a paradox here. I have maintained from the start you need extra dimensions to adequately describe these "energy free dynamics" of non-exchange of energy while in the state. You may argue that you do not need those dimensions and use parameters but you then MUST explain "cavity" resonances and interferences without the cavities if you are to use physics as I have done.

Those are the rules. In Quantum Mechanics you just have to make a "postulate" that this is the cavity you are having when there are no cavities. There is no answer in Quantum Mechanics for this it is a simple postulate you must make to start this "ball rolling". what I am saying is once you have done that and accepted this improbable state and see everything on the flat, then you are disallowed to see any phenomena in any more dimensions. That is a BOTTOM LINE to all arguments. Quantum Mechanics is a "Ptolemaic System" where Mechanism is not known but the results are excellent as long as we continue to work on the flat. On the flat it is a Lagrangian System with ordinary dynamics and energy conservation. Quantum Physics breaks this rule by having "stationary states"... in fact it is one big sucker of a stationary state. Think about what a stationary state means... no energy exchange... then ask why!!!

What I say is unless you concede that the mechanism is "higher dimensions" then you cannot adequately work with this problem and not before. You are all having two cents either way and not able to accept that you must leave the box before you can account for any extra physics that must be outside the box. We have discussed this all before and talked about the inner products but then the water becomes muddied by discussing traveling waves mixing in space and so on. Standing waves on the other hand requires confinement in a "box"... a "dimensional box". That is what makes this thing "go". Schroedinger's Equation describes cavities or wells... where are your cavities or wells around atoms in almost perfect "flatspace". The answer is it is not flatspace but a higher dimensional space. Everything flows from there....

Even Zephir and the Loop Quantum Gravity People (as crazy as it is rolleyes.gif it can only work in a confined state... they do it with gravity... lots and lots of gravity and gravitons... warping spacetime and quantizing it at the same time) understand that you must have confinement to enable the Physics. There are one or two major problems with this and that is all.

I must leave to go home now but think about this and comment on it please... I respect all of your opinions but we need to be "flexible". I will come back to it later.

Cheers

This post has been edited by Good Elf on Dec 20 2006, 06:58 AM


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Laserlight
Posted: Dec 20 2006, 07:48 AM


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Hi GE,

It is past midnite here so I will comment briefly. I am not quite sure what you
are driving at when you say I'm using multi-dimensional descriptions and
applying them to our space time (flat space?). There is nothing metaphysical
in any physical description that I used in my explanation.

QUOTE
You just cannot have standing waves in places where there are no cavities. This includes the dark space where we have placed the screen. Resonance and interferences leading to standing waves just cannot occur in the dimensional box of choice ... three dimensional flatspace plus time.


Do you agree that the slit "cavities" are basically miniature "waveguides",
when compared to the wavelength of light?

As "waveguides", which are nothing more than extended cavities, they have
inherent physical and geometric properties that affect the way that energy
acts within their "confines". True, they are not exactly "tuned" to the photon
wavelengths that pass thru them, but you must concede that they can
have dramatic influence on electro-magnetic fields due to proximity field effects.
Isn't this how diffraction, reflection, absorption, and scattering work. It is
energy interaction on an atomic scale.

Do you agree or disagree with the idea that matter vibrates/resonates at the
frequency of the dynamics operating at the atomic level?

Do you agree that 90 degree angled corners have a different natural energy
distribution than a flat surface because of the angle of exposure?

There is nothing extra-dimensional or metaphysical in these concepts, they are
well characterized natural phenomena existing in our space time.

That is basis of my explanation. I will be glad to debate you after some much
needed rest.

It is easier to respond to, and debate, direct questions. It takes far less energy
than trying to interpret veiled commentary with hidden innuendo.

I will read your commentary again, in the morning. Perhaps I will better
understand what you are trying to say then.
smile.gif

Regards,
LL
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Confused2
Posted: Dec 20 2006, 02:15 PM


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Hi LL et al,

The reason I keep posting the DSE equation is that we know this describes the result .. the explanation becomes (simply?) a matter of reverse engineering

I think a classical explanation would be along the lines of ..
1/Plane wave hits slits (see Maxwell EM wave for details)
2/ Huygens causes each slit to act as a new source with no phase change
3/ For interference pattern see ripple tank and/or DSE equation.

Comparing the above with LL's post here: http://forum.physorg.com/index.php?showtop...ndpost&p=156668

LL clarifies a point here http://forum.physorg.com/index.php?showtop...ndpost&p=156789
QUOTE (LL)

The EM fields of the arriving photons inductively couple to the fields of the cavities, and resonance takes place. The intensity of the resonance is directly proportional to the phase amplitude of the EM wave as it enters the cavity fields. The instantaneous amplitude of the arriving photon's EM field adds a specific amount of energy to the ambient fields. This energy coupling is a electrical transformer on an atomic scale. When energy harmonically couples between fields, there is a phase timing delay. Photon EM energy is coupled to the energy of the cavities and is then coupled/reflected back into the energy of the passing photon, but its phase timing has been shifted, The slight phase mismatch changes the energy of the photon's fields, its momentum, and its trajectory.


One (obvious?) point is that unless the phase of the 'wave' exiting the slit/cavity is shifted by 0,360,720.. degrees LL's explanation will fail. A challenge is to show that this condition is met .. or can somehow be evaded whilst still giving the same result.

Best wishes,

-C2.
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jal
Posted: Dec 20 2006, 02:45 PM


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Hi!
A quick comment ... got to run....
If we cannot measure it/see it .... do we call it a "hidden variable"?
My model uses a 2d surface. To describe what is happening do you need 12 dimensions?

Need to understand what is dimension in doing a proper description.
jal smile.gif


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Confused2
Posted: Dec 20 2006, 02:46 PM


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A while back D/L (last heard of heading for the archives) posted this applet

http://www.hmi.de/bereiche/info/dualismus/exp.java_en.html

(Click automatic calculation)

See the funny sinewavey things. TRoc (I think) suggested we needed a bit of uncertainty to make the peaks a bit blurry. Could the funny sinewavey things BE the uncertainty principle in action? Just a thought.

Best wishes,

-C2.

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yquantum
  Posted: Dec 20 2006, 04:13 PM


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C2, Good Elf, TRoc, LL, "THEY", "2, et al,

This is a very simple explanation of why we have to deal with such a large problematic issues as in measurement dealing with the DSE.

The UCP/T, entanglement, etc., is something we will need to live with until our experiment's/technology improves.

http://jersey.uoregon.edu/~imamura/208/jan27/hup.html

http://plato.stanford.edu/entries/qt-entangle/

Lisa, did you fall into a snow bank.
laugh.gif

ciao_
yquantum

BTW, Merry Christmas if it applies or just Happy Holidays if not. I hope to have a great Christmas and hope you do as well. wink.gif


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disce quasi semper victurus vive quasi cras moriturus
+ If you can't explain it simply, you don't understand it well enough.

This document was prepared as a service to the the physic community. Neither the United States Government nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, product, or process disclosed, or represents that its use would not infringe privately owned rights.
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Laserlight
Posted: Dec 20 2006, 05:31 PM


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Hi C2,

QUOTE
One (obvious?) point is that unless the phase of the 'wave' exiting the slit/cavity is shifted by 0,360,720.. degrees LL's explanation will fail. A challenge is to show that this condition is met .. or can somehow be evaded whilst still giving the same result.


I think you need to consider that a photon can be at any phase angle as
it enters and exits the slit "cavity". Remember that the mapped energy
of the EM fields is a sine wave. A photon can enter/exit the cavity at any
point of the 360 degree "circle" (any phase) of the sine wave. That means it can
arrive or depart during the positive part of the wave or the negative part of the
sine wave, but is "phase shifted" from its original entry phase angle due to the
energy coupling delays mentioned in the conceptual mechanics of the process.

Notice that a single slit prescribes a 360 degree phase circle on the screen evenly
split down the waveforms centerline. The width of the slit determines the
amount of diffraction (phase shifiting/delay). A narrower slit phase shifts (delays)
part of the wave more than a wide slit, and wave "scattering" occurs as viewed on the
screen. A wider slit has less phase shifting (more unshifted energy gets thru
without a delay) and a narrower wave pulse is projected, centered on the screen.

The dual slit experiment prescribes 2x the set of possible solutions. 1/2 of the
solutions always fall on 1 side of the screen centerline, or the other, according
to which 1/2 of the phase that they are in. There is always equal balance of
solutions on each 1/2 of the screen centerline.

Remember, the photon's EM field is still "rotating" as it propagates thru the cavity.
The frequency of the wave's rotation, and the physical "length" of the cavity, will
determine at which point in the rotational cycle that the delayed (phase shifted)
EM energy is added to the propagating wave function. This is the induced
phase delay, of the EM energy, by the cavity's electrically coupled harmonic
"transformer".

The induced harmonic signal timing delays, from the out of phase wavefunction,
that is created by the cavity, is either constructively or destructively added to the
propagating EM wave as it continues its angular rotation thru the geometry of the
cavity. This is the signal mixing point where phase addition or cancellation takes
place, IMO.

I can conceptually visualize the process in my mind, but trying to accurately
describe the "mechanics" is difficult to put into words so that others can also
visualize how it functions. Case in point. How do you describe the concept of
the color "red" to a blind man? It is very difficult, if not impossible. LOL!

I wish I could show it as a movie, then it would be clearly shown and readily
obvious.

biggrin.gif

Regards,
LL

This post has been edited by Laserlight on Dec 20 2006, 05:53 PM
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Good Elf
Posted: Dec 20 2006, 05:39 PM


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Hi Laserlight,

QUOTE (Laserlight)
Do you agree that the slit "cavities" are basically miniature "waveguides",
when compared to the wavelength of light?
Agreed... But what about atoms? These can be "solutions" of Schrodinger's Equation for a potential well.
QUOTE (Laserlight)
There is nothing extra-dimensional or metaphysical in these concepts, they are well characterized natural phenomena existing in our space time.
I never said there was anything "metaphysical" about atomic cavities. I think they would be standard science. But there is something already "metaphysical" in the "stationary states" which you have already accepted. You must admit that is a tad "spooky" don't you agree?

What I really disagree with is these cavities are in place because of permanent static charges on the atomic particles and have some other reason in free and open space. Two separate systems do you agree, when I would be expecting one and the same phenomena? One standing wave system appears to be the result of electrons and protons in space and the other occurs in the vacuum between the stars. In the charges explanation for these "cavities" theoretically (classically) they would simply continuously radiate energy away and the electrons would spiral into the nucleus if that is all they were. It just does not happen. Atoms would not be able to trap single photons either. I am focusing on the photons that are not "scattered" to lower frequencies by passing through the slots and being dephased. The ones I am interested in are the ones that continue on in the pristine quantum state. These are the ones that are part of the interference pattern on the screen. The others are not the "signal" but the "noise".

What I am attempting to convey is the "optics" of the propagation of the photon in time against the background of "cavities"... standing patterns in the space. For this one photon ... one at a time that remains in this quantum state, this pattern is fixed if the source and the sinks are static and the photon which may be spreading but retaining its temporal extension on the wavefront is internally "dynamically" inert due to time dilation. From the point of view of Special or General Relativity this space is very flat indeed so what actually exists between those "edges" and the screen. If we were to plot it like Confused2 would like to you will find the spatial volume filled with nodes and anti-nodes very much like this.
User posted image
In the nodes the photon cannot be detected at any time for the many of the photons that pass through them. Dephased photons might pass these points but that is another story. At the anti-nodes a photon may be located if a detector was placed there. Now do each of these points represent an instantaneous flux of equivalent energy or do the photons by-pass these regions altogether. Another option is the photons are not actually there at all. They are in a separate space to the "obstructions". They can even pass around these obstructions in higher dimensions if the obstruction is less than 1/2 a wavelength and in some cases even more.

Answering my own question the "particles" of light in "cavities" have one explanation, that is a resonance with the primal uncharged photons moving in "cavities". In the case of atoms ... atomic cavities not electrostatic charges in standing waves at all but EM waves in space. In the frame of the circulating "particles of light" there is no charge at all, there are no permanent sources of charge. In the case of pure propagation, waves of EM stressors. Sure we see charges but this is a topological effect seen in our "non-inertial" frame of reference where we see acceleration on the "charges". Charge is not the primary reason for the "stationary state". This is...
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In "free space" there are no charges to create this phenomena yet "stationary states" are there as well. It seems reasonable to say that all explanations for "stationary states" is a continuum from this Schrodinger Solution seen above on large cavities (up to the size of the Universe) to a similar Schrodinger Solution (for the same reasons) within the cavities of "tiny" atoms. In the end ... no such things as "permanent charge" only photons propagating in "vacuoles".

Cheers

This post has been edited by Good Elf on Dec 20 2006, 05:59 PM


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