What interference pattern of double-slit experiment does mean

[bhobba]

how it is happening? how single photon is showing interference pattern over the time period?

Because QM is a theory about what happens when something is observed, not about when its not being observed.

Here is the conceptual core of QM - forget about stuff you have read elsewhere - this is its core:
http://www.scottaaronson.com/democritus/lec9.html
'So, what is quantum mechanics? Even though it was discovered by physicists, it's not a physical theory in the same sense as electromagnetism or general relativity. In the usual "hierarchy of sciences" -- with biology at the top, then chemistry, then physics, then math -- quantum mechanics sits at a level between math and physics that I don't know a good name for. Basically, quantum mechanics is the operating system that other physical theories run on as application software (with the exception of general relativity, which hasn't yet been successfully ported to this particular OS). There's even a word for taking a physical theory and porting it to this OS: "to quantize."

Normally the double slit experiment is used to motivate the QM formalism, but really it should be the other way around - QM should explain it - and it does:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Of course the answer is expressed in the language of mathematics - sorry but physics is about mathematical models.

Basically QM is a variant on standard probability theory that allows continuous transformations between so called pure states:
http://arxiv.org/pdf/quant-ph/0101012.pdf

Consider flipping a coin. Probability theory describes the frequency of outcomes - but not what causes each outcome. Same with QM - it describes the frequency of outcomes - but not what causes any outcome. We simply do not know what that is - or even if there is a cause - nature may simply be like that. But regardless the QM formalism is silent about it. We have interpretations that speculate about it - but until there is some way to decide experimentally they are simply conjectures.

Thanks
Bill

 

[Cthugha]

If we let one photon pass through two-slit, photon will be detected some location at screen. if we continue the same for long time and sending one photon again and again, we can see the interference patterns in the detector screen.

how it is happening? how single photon is showing interference pattern over the time period?

As Simon Bridge absolutely correctly pointed out already, the pattern you see is rather a quastion of geometry. You see a double slit pattern because it is a double slit. If you have a different double slit, you will get a different pattern. If you start from the position of your light source and draw a line to some slit and draw another line from the slit to the detection plane, you will get some total path length for every point. If you do the same for the other slit, you will get a second path length for every position. Now you more or less get a map of the path length difference via the two slits for every single point in the detection plane. This path length difference of course translates to a phase difference. This map of phase difference versus position is what defines your interference pattern. Please note that it is really just the difference that matters. Independent of the initial phase you assume, the phase difference just depends on geometry.

Are we then in some sense preselecting the photons that get through?

Well, yes. Sure.

 

[naima]

Coherence is intimately related to indistinguishability. Whether you treat the problem classically or in a quantum way, you always add up all the fields/probability amplitudes leading to detection events at some position and get the modulus squared of them. By definition, interference means that some non-trivial pattern survives after averaging over many repetitions. This corresponds to some cross-product terms between fields surviving. So only fields with well defined relative phase in the average can give some contribution here. However, that also means that it is meaningless to attribute the corresponding detection event to just one of the fields. Both fields contributed to the detection event, so this situation automatically also results in indistinguishability. You cannot in principle trace the detected photon back to one of the initial fields, so talking about individual photons and their individual wave functions is somewhat dangerous. As a rule of thumb, all photons contained within a coherence volume (the volume inside which the phase of fields is so well defined that interference takes place) are indistinguishable.

It may be beneficial to visualize this as a single state of the field occupied by more than just one particle, rather than many individual photons. In the limit of many indistinguishable photons, that is usually well described by a coherent state with large photon number, which is the closest thing to a classical light beam that qm has to offer.

Does decoherence appear somewhere in the double slit experiment?

 

[Cthugha]

Does decoherence appear somewhere in the double slit experiment?

In the typical experiment with photons: No, they do not really interact with other stuff on their way. If you instead insist on doing the double slit with heavy molecules like C60 or want to do the experiment in a chamber full of incoherent scatterers, decoherence will matter.

 

[vijayantv]

Because QM is a theory about what happens when something is observed, not about when its not being observed.

ok, what is happening when we not observed? how interference pattern is generated while we are not observing?

http://www.scottaaronson.com/democritus/lec9.html

it doesn't say anything about double-slit.

http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

it doesn't tell about the single-particle interference over the time period. it tells only about single-photon is passing one time to two-slit and detected at the screen. (single time only)

one of ref. says that

" ----the maxima of this interference pattern are given by a formula familiar from wave optics."

and the conclusion: (it says about single photon is being sent one time).

"Quantum interference can occur only when a large number of identically prepared
particles are observed. These particles are detected at different locations, one at a time [9].
A single particle is always detected as a localized entity and no wave properties can be
discerned from it"

http://arxiv.org/pdf/quant-ph/0101012.pdf

it doesn't say anything about double-slit.

 

[DrChinese]

ok, what is happening when we not observed? how interference pattern is generated while we are not observing?

...

it doesn't say anything about double-slit.

The answers being provided are absolutely correct. The issue is that your questions either don't specify important details, or you are not understanding some of the deeper issues involved. It can be very difficult to jump from general statements to the specific when talking about QM.

You said: "I am lack of this kind of math. I came to know that single photon is showing interference pattern in two slit experiment by traveling into both slit at a time. and it causes two wave from each slit and these two waves are interfering and showing interference pattern."

And the answer is: when you do the math, the formula correctly predicts a probability of detection consistent with an interference pattern. That is what QM tells us.

You then ask: "what is happening when we not observed?"

And the answer is: QM is silent on that point. You are free to visualize it any way you find convenient. It would be reasonable to picture it as if 2 waves are interfering, as that matches the detection pattern. However, that is just a convenient and helpful picture and should not be taken too literally.

You can ask all you like as to "what is really happening?" but no one really claims to know exactly. All that QM provides is predictions for experiments you can set up and observe results. It does a great job at that. So you need to phrase your questions in that form if you want solid answers.

 

[jtbell]

Because QM is a theory about what happens when something is observed, not about when its not being observed.

ok, what is happening when we not observed? how interference pattern is generated while we are not observing?

Bill answered this question, to the best of our knowledge, later in that post. I've put the key parts in boldface:

Consider flipping a coin. Probability theory describes the frequency of outcomes - but not what causes each outcome. Same with QM - it describes the frequency of outcomes - but not what causes any outcome. We simply do not know what that is - or even if there is a cause - nature may simply be like that. But regardless the QM formalism is silent about it. We have interpretations that speculate about it - but until there is some way to decide experimentally they are simply conjectures.

On this forum, some people love to debate about these conjectures (interpretations). Look for things like "Bohmian mechanics", "many-worlds", etc. However, until someone can come up with a way to decide between them by experiment (which at this moment doesn't appear to be possible even in principle), arguments for and against them end up based on personal philosophical preferences about the way the universe "should" work.

 

[vanhees71]

The question, what's the meaning of observation in the sense of quantum physics is not so trivial as it might seem. There are a lot of pretty "esoteric" claims even by very famous people. E.g., John von Neumann, who was the first to give a mathematically strict formulation of non-relativistic quantum mechanics, revealing the Hilbert-space structure, applying the spectral theorems for non-bound self-adjoint operators to make sense of continuous spectra, etc. had ideas about the "measurement problem" which sound very strange (at least to me). It's known as the Princeton interpretation of quantum mechanics, and I don't want to get into any detail about this. The upshot is that he thinks the result of a measurement is established only when a conscious mind has become aware of it. For further details have a look at

https://en.wikipedia.org/wiki/Von_Neumann–Wigner_interpretation

In my opinion that's nonsense. Nowadays the experimentalists, say at the LHC doing experiments in ultrarelativistic proton-proton or heavy-ion scatttering, take notice of the outcome of an experiments much later than it was done. The results of the measurement are the momenta of zillions of produced particles in all kinds of detectors in the big experiments (ATLAS, CMS, LHCb, ALICE) in form of data in huge computer files. Then the experimentalists uses these "raw data" from the computer file and analyzes them, making plots etc. Then we get aware of what's come out, e.g., that in certain invariant-mass distributions after careful background subtraction and statistical analysis "a Higgs-boson like particle is seen".

In my opinion, it's very mondane, when an observation is made: It's made at the moment when the observable of interest of the quantum system (say an elementary particle) is somehow registered by a macroscopic measurement device and this information is somehow irreversibly stored.

This is not very different as with any probabilistic experiment. Throwing a die leads with some chance to a number between 1,...,6 which is practically unpredictable and thus can be seen as a probability experiment. If the die is not manipulated the probability to get a certain result is 1/6, and this can be tested repeating many (uncorrelated) experiments, and we can give a significance in how far the prediction of the probability 1/6 for each possible outcome is true or not. The more often we repeat the experiment the better we can tell whether the probabilistic prediction is compatible with the experiment or not.

The difference to the quantum mechanical probability is just that according to quantum mechanics, even when we know everything about the quantum system, i.e., we have prepared it in some pure state, not all observables have a determined value. This is not due to some lack of knowledge about the state of the system but because, according to quantum theory, the observable has no determined value due to the preparation of the system in the pure state. Knowing the pure state only tells us the probability to find a certain value when an observable is measured, and again we can make a probability experiment by repeating the measurement of the observable many times, the more often the better. A certain value of the observable is known as soon it is measured by an appropriate (macroscopic) device and this information somehow stored so that we can take notice of it, as in the example of throwing dice. For the double-slit experiment the particle's position is established as soon as it hits the screen, and you can count the pixels on your photo plate (or CCD in a more modern lab) to figure out, whether the predictions of quantum theory are correct with regard to the position probability distribution of not, and the more particles you run through the apparatus the more precise becomes your statistical significance for success or failure of this prediction.

This is the socalled minimal statistical interpretation, which is the one making the least assumptions and which is, in my opinion, the most natural one. Of course, it's a bit disappointing that we don't know more about the system than the probabilities for the outcome of a measurement, but that's how Nature seems to be, according to quantum theory. Physics doesn't provide explanations for why Nature is as it is but only describes, how Nature is (or at least that part of Nature that is objectively and reproducibly established by observations).

 

[vijayantv]

You are free to visualize it any way you find convenient. It would be reasonable to picture it as if 2 waves are interfering, as that matches the detection pattern. However, that is just a convenient and helpful picture and should not be taken too literally.

Wiki says that it is caused by two probability wave

http://en.wikipedia.org/wiki/Double-slit_experiment
The appearance of interference built up from individual photons could seemingly be explained by assuming that a single photon has its own associated wavefront that passes through both slits, and that the single photon will show up on the detector screen according to the net probability values resulting from the co-incidence of the two probability waves coming by way of the two slits

Professor Benjamin Schumacher also says that the interference is the constructive and destructive pattern of two waves.
http://www.youtube.com/watch?v=7y5RJHiDOK8

and in many other places.

are all wrong? isn't the interference is caused by to wave?

 

[naima]

Can we say that an event is a measure when it gives a "robust mark" which can be read?
The mark is robust when it contains many duplicate copies of the same information.

 

[Dale]

vijayantv, your question is asked and answered.