Problem with the two slit experiment, Observing later

I have a thought on the two slit experiment with an electron. What if I set up the two slit experiment so I indirectly measure whether an electron passes through one slit or the other slit, but rather than observing the measurement, I simply have the equipment record the result. After the experiment runs for a period of time I look at the screen recording the result of my experiment. The result will either be an interference pattern or it will indicate a result showing that the electrons discretely passed through one slit or the other slit.

If it is an interference pattern, I will then examine the results of my recording device. The recording device will have to show me that the electrons passed through one slit or the other, which then means I cannot have found an interference pattern. If it is a pattern showing the discrete passage of electrons through one slit or the other, then I destroy the record of my measurement equipment, which means that I will never have observed the results so that then I should have found an interference pattern on the screen.

How is this possible?

You don't have to look because it is not an observer created reality. What do you think the real answer is?
I'll tell you.
Its simple. Its a phenomenon.
Sometimes there is no matter wave.

Indirectly? :-) You have already measured the particles, whether you look at the results or not, and will never see any interference.

http://en.wikipedia.org/wiki/Double-slit_experiment

A remarkable result follows from a variation of the double-slit experiment in which detectors is placed in each of the two slits, in an attempt to determine which slit the photon passes through on its way to the screen. Placing a detector even in just one of the slits will result in the disappearance of the interference pattern. The detection of a photon involves a physical interaction between the photon and the detector of the sort that physically changes the detector.

-C2.

Hi wesden, Confused2, Neuro, Nick et al,

An even more remarkable experiment is
the Delayed Choice Quantum Eraser Experiment
Now this can be performed by photons but the result will be the same as when using electrons except the slits would need to be very much closer to notice diffraction. Here we see as noted in our time frame an event that has occurred long after the "destruction" of a photon affects the result of the "destroyed" photon being part of a diffraction pattern or not. Using entangled pairs of "matched" photons if the slit one of the entangled photons passed through is known, it's "twin" will "de-cohere" and form part of an "ensemble" of photons that contain no interference pattern. This "test" can occur long after the original photon impacted on the screen. From an observer point of view this means that an "event" that happens later in "history" can affect the past. This is like saying that filling out a questionnaire today can affect the result of a poll that was counted and published in 1900.

Of course this is a quantum event and is not to be directly compared with the example I have just given. Nevertheless an amazing result.

Here is something else that may amuse you taken from Paul Dirac when speaking about this same double slit experiment...

(my emphasis) That will give me something to think about very carefully. It is all about "bosons" and Bose-Einstein Statistics, and this crops up all the time with LASER action. No such thing as truly "destructive" interference. Love it!

Cheers

This post has been edited by Good Elf on Sep 23 2006, 04:44 AM

Good Elf etc,

.......Along similar 'lines', although not dealing with time; I predict within 500 years (with the help of AI) we'll have the technology to manipulate what we term
"quantum universe", with say.... a single particle!, an electron perhaps.
A shade like the butterfly effect.....but by making this electron dance in a
controlled fashion, an interactive cosmic 'resonance' response will allow us to
create things "just like magic"........totally the same principle as the Rain Dance or a set ritual etc, but it'll be something scientific and actual instead of a load of hocus-pocus. I think we've 'spiritually' always known of this potential technology and this confuses the hell outta me as I'm > a little skeptical with religion etc. I really don't do Gods, but as you are aware everything is connected, this is why Buddhism has for me 'a certain appeal'. Perhaps what we term 'spirituality'
is merely inherent subconscious guidance from the multiverse?....then again, maybe I need locking up!
Imagine one day with this 'fruitcake' technology....all things might be created at
the press of a button....or even a mere thought (The Forbidden Planet ).

We're a very young intelligent species set to change ourselves beyond
recognition, in terms of what we generally define as life. However, innumerous
species throught the multiverse may have already taken this next step and might
have already established this technological art...Yep, but we've no access to it ....but even this might not be true, as now and again miracles occur ....is it just the action of random chance?....yer.... probably.

This post has been edited by fivedoughnut on Sep 24 2006, 04:40 AM

Hi fivedoughnut,

"Would you like fries with that?"

It really does not matter what we can do... I am sure that there are many things we could do. The important question is what we may become. Before you fall on your knees in front of a mirror to worship... take a long pause and realize just what we are first and contemplate just who is going to exercise this "godlike" power and over what?

Our social system is "promoting" only the most violent and aggressive and power hungry individuals to rule. My suggestion is this amount of 'control" is incompatible with a benign "dictator". The centralization of World power will eventually end up with winners and losers. I think there are enough losers on this Earth already to go around. I like "games" but the kind of games evil people like to play are not nice games are they?

To me you should consider well what you wish for because you may get it. You call us a young and intelligent species but in my opinion most of us are not that intelligent and cannot make our own way by ourselves in the World. We still want "leaders" or better still "gods". Is this what you mean by intelligent? Actually we are just smart "apes" and a unique experiment on a World to see if this evolutionary line is capable of solving any of the problems and survive. So far we have neither been able to control our greed nor our numbers on the surface of this World. I do think that Science is "self limiting" and you are right ... everything is connected and we are on the edge of exterminating the majority of kindred species who share our genetic code on the surface of the planet. We also seem unable to stop ourselves suffering the same fate as others. Yes I know some will always survive ... but will it be yourself or your progeny or neither?

You mention "Forbidden Planet"... the mighty Krell at the height of their achievements were destroyed in a single night by the "mindless primitive" inside of all of them.
Wikipedia: Forbidden Planet
If we do not change I think this is the fate of all of us... at the peak of our hubris. Random chance?... hardly!

Last question... can you pick the "human" in this picture?


Cheers

Thanks for that Cobber

You're right though.....whatta bunch of silly animals we are...perhaps this could somehow be genetically engineered out?..... a little frightening in concept as we'd dehumanize ourselves.

'scuse me now, I've a full length mirror to worship...Gaffaw, etc

Hi fivedoughnut, wesden, Nick, Confused2, Neuro et al,

Well that killed the discussion didn't it. I hope people (fivedoughnut) did not think that I was chiding anyone. I was making a comment about how we are going about things without having the correct level of "humility".

Anyway back to the double slit experiment... It is pretty clear that the Uncertainty Principle is not related directly to anything that is magical about quanta. It is related to just about anything that can be measured which has duration and energy...
Heisenberg uncertainty principle - measurement limits - reciprocity relations related to Fourier Transforms
While this is about measuring bursts of EM radiation as the article demonstrates if you convert the sync function to "power" by squaring the magnitude you conveniently get the same pattern as you would have with the double slit experiment. And further... as the article indicates... this is no "coincidence". It is the same phenomenon... underneath it all.
Time Domain
Frequency Domain


Cheers

At last .. Laplace transforms on the web in a sensible form .

This is just intended as a marker for what I think is the 'right' maths to analyse the problem.

http://people.deas.harvard.edu/~jones/es15...laplace.html%20

What we need is the convolution of the sine wave and the gate pulse .. they are both included. By 'magic' multiplying the Laplace transforms gives us the convolution of the two functions.

With luck the applet does the inverse transform and plots the result.

All perfectly analytic .. no uncertainty.

If anyone wants to have a go.. carry on. If not I'll come back to this when I've finished my Income Tax Return .

-C2.

***
I think the problem lies in genuine 'physical' uncertainty.. I


This post has been edited by Confused2 on Sep 27 2006, 12:45 PM

Hi Hi Confused2, fivedoughnut, wesden, Nick, Neuro et al,

There are more than one way to skin a cat. Laplace Transforms are a useful technique. Solutions are available as we all know,

What you are seeking is this... right?

"There is a reciprocity relation between convolution in the time domain and its counterpart in the frequency domain. That is, convolution in the frequency domain becomes a multiplication in the time (or space) domain. This is sometimes called the "frequency domain convolution theorem." Here is your "gated sinewave"...
Figure 4.8 illustrates this result using cosine and rectangle functions in the time domain.
We have both seen this before...
Convolution Theorem
Is there something I am missing here. Are you suggesting that the analysis supplied is wrong or that there is "more" and something far more mysterious than just an indeterminacy when we measure things?

Compare and contrast these two versions of the "same information" from some pages off the Harvard Site...
Optical Analog of Uncertainty Principle... single slit diffraction pattern
Heisenberg Uncertainty Principle... single-slit diffraction pattern

The double slit interference pattern is "another layer" of analysis on top of this single slit phenomenon where two single slit diffraction patterns interfere with each other in phase but displaced by the relevant slit separation. The image on the screen is the "square" of this "projection". What is not usually stated in most of this analysis is that each individual photon undergoes this process and passes through both slits while still a spreading wave.

Here is the single photon double slit interference with itself and a form of the Quantum Eraser Experiment (without the delayed choice)
Single Photon Interference
As you can see individual photons do not "destructively" interfere with each other for this to work correctly... as "true bosons" they only interfere with themselves (individually). Each individual photon "explores" the entire possible "landscape" before it strikes the target just as Feynman suggests.

Cheers

This post has been edited by Good Elf on Sep 27 2006, 03:41 PM

Hi Good_Elf, fivedoughnut, wesden, Nick, Neuro et al,

I'd have to check whether a Fourier analysis is inherently lossless .. I'm not saying it is .. just need to think about it. The Laplace transform should certainly be lossless (is that a word?) .. hence .. wherein lies the uncertainty? Even if you limit the bandwidth .. you just get 'another transform' .. still reversible and still no loss. You need a non-analysable function (kinda struggling for the right words there) to get 'loss' or 'uncertainty' .. the references cited so far do not make this clear.

We agree the Fourier (or Laplace transforms) are fun.

Why does the photon turn up in one place one time and somewhere else another time? Isn't that what an analysis of the double slit experiment seeks to answer? How does a lossless analysis help? There is something else going on .. is there not?

Personally I would prefer to establish a way to analyse the most basic two slit experiment before attempting the delayed quantum eraser version .. it should be a good test of theory.

Best wishes,

C2.

Hi Confused2,

He he he... I think I get that. When dealing with any function in nature there will be ways to represent it using various functions. Laplace Transform is one form of representation and it is without "technical" error. But show me any function in nature and I can be certain that it is not "perfect" and you will need to approximate it with a series (of some kind) This will always resolve itself into a measurement then a substitution of that measurement for the "real" function that is found in nature. In their own way Fourier Transforms are "perfect" in representing harmonic series for any particular variation in a parameter. It is just "natural" to choose Fourier Transforms over Walsh Transforms or some other representations because this is a physical system.

You bet your little blue booties!

A single photon can only end up in one place no matter how much it diffracts. In the end there can only be one interaction where the qubit is lost (Ignoring OAM). After that point it is a completely new problem. This diffraction cannot be seen directly and only these quantum demolition events can determine that the photon has previously undergone diffraction at all.

The delayed choice QE is a far more complicated problem. Above I mentioned only the simpler problem of determination that we know collapses the state. The determination of "which way" is enough to destroy the state in any diffraction event. When you think about it since each individual photon actually goes through both slits detecting it passing through one slit must affect the "pattern" it would have formed by passage through the other slit and interference with itself.


Cheers

Hi Good_Elf et al,

Very sorry , I don't seem to have said what I intended. It's probably on my Tax Return form somewhere.

Please forgive me for having another go..

4 posts in 1 really.

GE reference 'Establishing reciprocity limits by Fourier transforms'
http://www.fas.harvard.edu/%7Escdiroff/lds...yPrinciple.html

Same maths but is it the same physics? The result (shown) is absolutely predictable. I just don't see analogue for the Uncertainty Principle here. What or where is the representation of 'uncertainty' in the result?

***************************************

Of the 2 slit experiment itself..

1/ Why is the result of the 2 slit experiment not completely predictable when the photon can pass freely through the slits without being detected, I'll call this the two slit interference result.

2/ Why does detection of the photon at one or other slit (as it passes) change the statistical outcome from double slit to that of a single slit (That's the easy one?)

3/ Detecting (later) which slit the photon passed through apparently changes the experiment from a 2 slit interference experiment to a single slit experiment.

If the answers to 1/ and 2/ do not predict the answer to 3/ then our answers to 1/ and/or 2/ are wrong. We need to keep refining our answers to 1/ and 2/ until they predict 3/

Does that makes sense to anyone?

-C2.

********************************************************************

Sorry GE..

Summary
A single photon can only end up in one place
A single photon can only be detected once
Once detected it is a new problem
Until you detect a photon you cannot say anything about where it has been. [ C2 note .. I'd add .. even after you detect a photon you cannot say how it go there .. agree?) ]

Assuming this is the answer to 1/ and or 2/ .. does it predict an answer to 3/ ?

-C2.

**********************************************************

As a point of interest.. another alternative might be to look at the delayed detection result as a form of quantum computer .. if other analysis fails.

-C2.

Hi Confused2,

Well this is very hard to show but it is in the measurement of the system that you will have uncertainty. Remember you do not actually know the nature of any source or measurable until you actually physically measure it. There would be two extremes between which the real function would lie. Your measurements will disturb this "absolute" value enough to result in two extreme solutions for the value of the coefficients in the Fourier Series. Between these two "extremes" will be the uncertainty in the measurement. There really is no uncertainty until you try and measure the nature of this source. The uncertainty is not in a "function" like cosine or an exponential function. The function could have an "exact" expression. It is only in trying to measure what it really is.

Many point to an "inherent" chaos in spacetime being the "resolution". This can equally be stated as the inability to measure one variable with infinite accuracy without disturbing the other variable (infinitely).

1/ It is completely predictable ... just plug in the "exact" relationships that will be measured and that will be the "exact" solution.
2/ It is completely predictable when you use wave optics. It is the result of summing vectorially two perfect "exact" single slit "waves" to give the one interference result. The rub is you do not know the size of the slits, their separation nor the nature of the source accurately enough until you measure them in an experiment.
3/ My opinion is the universe is "perfect", there is no granularity at the Planck Limit, it is our measurements to determine its true nature that are not perfect because it disturbs the universe through "detecting" it. In actual fact there is no way to tell this is not the real case... a philosophical mindset is what stands between the two and understanding the true nature of experimental measurement.

We are "blind" to anything in our universe until we attempt to "see" what is there. What is there can only be determined through measurement of its physical parameters. The disturbance we use to see things is "light" or "electromagnetism" even down to one photon at a time and the position of an object can only be determined down to the limit of the Rayleigh Criterion.
Wikipedia: Angular resolution
This is entirely consistent with being able to resolve an object only down to the limit of a fraction of a wavelength. This is the minimum spatial resolution. Different photons scatter to different extent and lead to different estimates of position. To get better measurements of position we use more energetic photons which disturb the position of what is measured sufficiently to upset its energy (kinetic or potential).

Despite what people say if you confine the "source" to a lightproof cavity and cool the cavity to a very low temperature and only use the "best" coherent light, You can then use a series of pinhole apertures to restrict the radiation to that coming from a small area of space. Despite what quantum theory says about indeterminacy... photons will not just pop in from alpha centauri at pure random to interfere on the back of the screen. You know just what I have said about boson states and "coherency" so it comes as no surprise that you can reduce the noise to a very low figure and still arrive at "indeterminacy" through actually having to measure the system variables. In the end Physics must come down to a measurement not just a bit of pure mathematics. That is the real nature of our Universe... it is all measurements after all.

Of course it is a form of quantum computer. Think of space as being a cavity that is resonant and everything in it also subject to resonance. A single measurement inside the cavity will not "immediately" tell you what is happening in all other places in the cavity. However it actually is telling us that information because the single photon is "exploring" the entire cavity and if we could tell the total shape of the self-interference of a single (monochromatic) photon ... "with itself"... we would know the shape and extent of the cavity "everywhere" the photon can go, up to a Rayleigh Criterion of that space. This is like taking an "impulse" (a sudden "pop" with ideal characteristics) such as in mining or seismic geophysical investigations and recording the echoes as they return to an array of strategically placed detectors. The original "impulsive" signal (containing an infinite number of frequencies) has an almost zero width in time (a spike) and a high specific energy and the recordings in time at the sensors (geophones) of the spread out echoes in time, is the response of the "cavity" to this "stimulation" (a black box). An "astute" analysis of this information could recover the "landscape" of the signal and all possible paths that were traveled on. This is also similar to Sonar. Indeed this is the same as side scan or aperture scan microwave or infra-red or even optical arrays. Beautiful examples of high technology. These utilize the property of phase both temporally and spatially. There is the reverse problem such as directed energy weapons...
Wikipedia: Directed-energy weapon
These match the cavity of space to the burst of energy to the target. It could be made "almost exact" that the cavity can be used to focus the energy on a target with a very astute phased "excitation" of an array having a total understanding of the "instantaneous shape of the cavity", not just what many consider just the path. Once you have that level of understanding and control over the different Fourier components in both frequency and phase (spatial and temporal) and the exact knowledge of the cavity, the inverse problem can be computed to deliver any kind of signal you want to a target... even to the other side of a wall if you like.

So "volumetric space and its shape" is a kind of computer... an analog computer... that is the full technical specification of the space (in time) that determines how the cavity "rings" under excitation by one or by many photons. The bells... the bells...

After all... the Universe is actually a cavity too. The double slit experiment is like having a "musical instrument" with a number of openings that resonate in the many modes of excitation... like a flute. It doesn't work nearly as well without the holes. But like a "flute", there are many possible excitations, each one telling us something more about the overall cavity (different frequencies of light produce different interference patterns, each one is predictable for a particular "fixed cavity"). It is only now with our "advanced" means of computation could it be possible to determine how a complex system responds "everywhere" accurately enough to transport energy in the fashion we may wish... the science of photonics and of quantum computing and tunneling.

Cheers

This post has been edited by Good Elf on Sep 29 2006, 05:41 PM