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Quantum behaviour and the double-slit experiment.
I have seen it stated that the quantum entities approach the double slit as a 'probability wave' and that this accounts for the appearance of the interference lines on the receiving screen. It does seem to me that a probability wave must necessarily have no troughs - and, indeed only one peak. This being so, I fail to understand how probability waves could possibly produce interference fringes. To argue, also, that the approaching effects are somehow 'unreal' waves, leaves me entirely unconvinced; they are conveniently real enough to produce the observed interference effects!
Can anyone clarify my thoughts? I'd be most grateful for help.
Can anyone clarify my thoughts? I'd be most grateful for help.
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.Joeloki
Why do you say a probability wave "must have no troughs and indeed only one peak"?
That said: The experiment shows ( and this is not a thought experiment but a real experiment tested many, many times) that where there are no observers a single particle leaving the gun will create interference consistent with travelling through both slits at the same time like a wave. If one slit is closed or an observer checks to see which slit the particle passed through it causes the wave function to collapse and the result is expected behaviour of a particle. The implication of this is that the particle seems to have knowledge of the whole experiment. So without observation the particle follows paths based on probabilities unless it is observed when it will only follow the observed path and will not follow any other paths. Or in other words, the particle is not real until it has been observed.
I'm not surprised you are confused I don't think anyone actually understands why this happens
Why do you say a probability wave "must have no troughs and indeed only one peak"?
That said: The experiment shows ( and this is not a thought experiment but a real experiment tested many, many times) that where there are no observers a single particle leaving the gun will create interference consistent with travelling through both slits at the same time like a wave. If one slit is closed or an observer checks to see which slit the particle passed through it causes the wave function to collapse and the result is expected behaviour of a particle. The implication of this is that the particle seems to have knowledge of the whole experiment. So without observation the particle follows paths based on probabilities unless it is observed when it will only follow the observed path and will not follow any other paths. Or in other words, the particle is not real until it has been observed.
I'm not surprised you are confused I don't think anyone actually understands why this happens
Lets take a specific example:
Electrons classically thought of as particles incident on double slits.
Result: interference patterns - a bit head scratching but we consider that as photons can behave as particles electrons can behave as waves and so they must interfere.
Now slowing down the elctron rate so that only one at a time can hit the slits we still get interference!
So how can this be? Under the Copenhagen interpretation ( http://en.wikipedia.org/wiki/Copenhagen_Interp retation ) the experiment resolves into a probability density of finding electons within specific locations and at some points that is zero.
I dont see why you think the probability function must have 1 peak and no troughs (as if there were a single slit ) why do you think that?
Electrons classically thought of as particles incident on double slits.
Result: interference patterns - a bit head scratching but we consider that as photons can behave as particles electrons can behave as waves and so they must interfere.
Now slowing down the elctron rate so that only one at a time can hit the slits we still get interference!
So how can this be? Under the Copenhagen interpretation ( http://en.wikipedia.org/wiki/Copenhagen_Interp retation ) the experiment resolves into a probability density of finding electons within specific locations and at some points that is zero.
I dont see why you think the probability function must have 1 peak and no troughs (as if there were a single slit ) why do you think that?
Thankyou for your splendid answers!
The reason I think that the probability wave has no troughs and but one peak is 'commonsense' (?). The minimum probability of an event must be zero - it can have no negative value - hence the wave can have no troughs which bring the probability below zero. I visualise the wave to be in the form of a normal distribution but maybe I'm too simple-minded!
Another point: a single quantum passing through the two slits does not show an interference pattern: it shows a dot. Only when a stream of quanta flow does an interference pattern appear.
The reason I think that the probability wave has no troughs and but one peak is 'commonsense' (?). The minimum probability of an event must be zero - it can have no negative value - hence the wave can have no troughs which bring the probability below zero. I visualise the wave to be in the form of a normal distribution but maybe I'm too simple-minded!
Another point: a single quantum passing through the two slits does not show an interference pattern: it shows a dot. Only when a stream of quanta flow does an interference pattern appear.
I see from your quotes and question mark you've spotted the irony of mixing common sense and quandum mechanics!
The system must be defined by the schrodinger equation which gives you what is called the wave function psi this is a complex scalar field and may vary with time and position. The probability is actually given by the square of this which removes the complex numbers.
So it's a little more complex
The schrodinder article on Wikipedia is a bit complex this is a bit more accessable
http://www.physlink.com/Education/AskExperts/a e329.cfm
The system must be defined by the schrodinger equation which gives you what is called the wave function psi this is a complex scalar field and may vary with time and position. The probability is actually given by the square of this which removes the complex numbers.
So it's a little more complex
The schrodinder article on Wikipedia is a bit complex this is a bit more accessable
http://www.physlink.com/Education/AskExperts/a e329.cfm
Hi Jake
And how very strange it all is. In fact, I think the interference is there regardless of how it is interpreted and this is very wierd in itself.
The wave (i think) is a result of the probability of finding an electron or photon in a particular position. Because the range of probabilities of finding a particle in a particular position ranges from highly probable to not very probable it can be represented by a wave function. Since there are two slits the particle travels through both slits, as would a wave, and arrives at the detector screen. As with actual waves, the results show interference where there is an overlap of waves. (i'm happy to be corrected on this) According to John Gribbon this is interpreted in the Copenhagen Interpretation thus: "The interference of probabilities can be interpreted as if the electron vanishes once it leaves the gun and is replaced by an array of ghost electrons that each follows a different path to the detector screen. The ghosts interfere with one another and when we look at the way the electrons are detected on the screen we then find the traces of this interference, even if we deal with only one electron at a time... Each of the ghosts corresponds to a packet of waves that Born interpreted as a measure of probability. The Observation... is equivilent.. to the disapearance of all of the array of probability waves except for one packet of waves that describes one real electron.This is called the collapse of the wave function."
Truth is stranger than fiction.
D
And how very strange it all is. In fact, I think the interference is there regardless of how it is interpreted and this is very wierd in itself.
The wave (i think) is a result of the probability of finding an electron or photon in a particular position. Because the range of probabilities of finding a particle in a particular position ranges from highly probable to not very probable it can be represented by a wave function. Since there are two slits the particle travels through both slits, as would a wave, and arrives at the detector screen. As with actual waves, the results show interference where there is an overlap of waves. (i'm happy to be corrected on this) According to John Gribbon this is interpreted in the Copenhagen Interpretation thus: "The interference of probabilities can be interpreted as if the electron vanishes once it leaves the gun and is replaced by an array of ghost electrons that each follows a different path to the detector screen. The ghosts interfere with one another and when we look at the way the electrons are detected on the screen we then find the traces of this interference, even if we deal with only one electron at a time... Each of the ghosts corresponds to a packet of waves that Born interpreted as a measure of probability. The Observation... is equivilent.. to the disapearance of all of the array of probability waves except for one packet of waves that describes one real electron.This is called the collapse of the wave function."
Truth is stranger than fiction.
D
Perhaps I am going away at a tangent from the direction of my original question, but the topic seems to invite a diversion. When I said that a single quantum passing through the double slit does not show an interference pattern, it shows a dot, I believe this to be true. It seems to be part of the accepted intelligence that because a stream of particles produce an interference pattern, that each individual item must necessarily interfere. This may be true (and probably is!) but I venture to challenge the word of the gods! Where is the logical step between the behaviour of the mob and the behaviour of each individual particle? I stick to my guns: a single particle does not show an interference pattern: it shows a dot. This is not to say that an individual quantum does not interfere with itself - it may well do so - but where is the proof? Yes, truth may be stranger than fiction, but are we sure it is the truth?
You are correct Joeloke to state that in order to get the results we must add up the dots. One photon or one electron does indeed simply make one mark. However, the "Proof" comes in the observation (or lack of it). If we do not observe the particle going through a slit the pattern built up is of each particle going through both slits. If we observe the particles going through particular slits the pattern that builds up has no interference. This shows that observation has changed the behaviour of each particle
Perhaps observing the point of a single particle on the detector screen also collapses the wave function.
Perhaps observing the point of a single particle on the detector screen also collapses the wave function.
Thankyou Dawkins and Jake-the-Peg. I must surely have exhausted your patience by now but I'd like you to know that I have appreciated your efforts. You have been most helpful in the formulation of my understanding of the double-slit experiment.
Thanks to JustSia also. you may be sure that I'll use your reference!
Thanks to JustSia also. you may be sure that I'll use your reference!
Anyone involved in this thread might be interested in this link. It is an interview with the scientist Carver Mead which brings some of our received assumptions about 'quantum wierdness' down to earth. http://www.laputanlogic.com/articles/2003/09/2 1-106446538310636532.html
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