If we shoot one electron or photon at a time to a double slit for a long time, interference pattern will build up on the other side. If the gap between each electron or photon is long enough that they don't interfere it appears that a single electron or photon is interfering with itself. So, is the interference pattern obtained by shooting only one electron or photon its just that we can't see the pattern because its too dim and so we have to shoot many electrons or photons one after the other to make the pattern brighter?
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asked Mar 16, 2015 at 18:54
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$\begingroup$ The particle certainly interferes with itself in the sense that it can easily show up at a spot on the detector that it could not have reached if only one slit were open. $\endgroup$– WillOMar 17, 2015 at 0:26
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$\begingroup$ @WillO: This is not right. Not only behind two ore multi slits you see fringes but also behind one slit and behind everey edge too. $\endgroup$– HolgerFiedlerApr 14, 2015 at 3:42
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$\begingroup$ @HolgerFiedler: Thanks. I should have said: "It can easily have a high probability of showing up at a spot on the detector where it would have been very unlikely to land if either of the two slits had been the only one open". Does this seem okay to you? $\endgroup$– WillOApr 14, 2015 at 3:48
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$\begingroup$ @WillO: Yes usually the effect from the edges will be reinforced.But, not to be to sophisticated, this depends on the well or not well designed slit's distances, the slit's width and the distance of the observers screen. $\endgroup$– HolgerFiedlerApr 14, 2015 at 3:55
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$\begingroup$ a pattern needs a lot of dots, hence many shoots. It seems impossible to know at which statistic an individual photon will be related. What is you idea ? $\endgroup$– user46925Jun 7, 2015 at 22:46
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5 Answers
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Short answer: no. The interference pattern is formed only after many electrons are shot through the slits. The "natural" conclusion of this experiment is that we cannot predict where an electron will be detected, only the probability of the electron being detected in particular locations, as indicated by the interference pattern. Another remarkable aspect of this outcome is that it is indicative of wave-particle duality. The single point of detection when shooting a single electron suggests particle-like properties, whereas the interference pattern suggests wave-like properties.
https://www.youtube.com/watch?v=MbLzh1Y9POQ (an excellent real-life video showing the build-up of the interference pattern)
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You can't predict where the electron will hit, but you can measure that it will hit at some discrete point. The probability distribution of final positions on the detector corresponds to the interference pattern.
You will see the pattern only after shooting many electrons:
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The electron is an elementary particle.
Elementary particles are point particles - they have no extent. This is a basic postulate in the Standard Model of particle physics that has been tested over and over again the past fifty years.
When experimenting with elementary particles, we have to use quantum mechanics. It is proven beyond doubt that classical physics and classical concepts are unable to explain the experimental behavior of elementary particles and composites in dimensions commensurate to $\hbar$ of the Heisenberg uncertainty principle.
In quantum mechanics, predictions about the behavior of particles are made by solving boundary value problems with the quantum mechanical equations, but the solutions are not trajectories. The solutions describe the probability of finding an elementary particle at a specific (x,y,z) for the given boundary conditions. Because solutions of the QM equations are sinusoidal, the probability has a wave nature and can display interference patterns, as seen in the single electron two slit experiment. The accumulation of electrons on the screen reflects the probability distribution of an electron impinging on the boundaries of two slits to be found at each (x,y) of the screen.
In contrast to water waves, which are built up by energy transfers on the molecules of the water, the energy of the electron is localized at a point. The location of that point cannot be calculated in advance by using the only tools we have to study elementary particles - quantum mechanics. Only the probability of the electron's existence at that point can be calculated.
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$\begingroup$ "This is a basic postulate in the standard model of particle physics": can you give a reference to this, and in what sense this is true? Do you mean "no spatial extent" or in the sense of there being e.g. one electron momentum eigenstates which are lone points in the corresponding momentum space? I'm not questioning this: I have heard this statement many times but my layperson's knowledge of the SM is basically limited to the notion of particles as irreducible reps of the Poincaré group, my intellectual wherewithal swiftly dies beyond this notion and I can't seem to find a reference. $\endgroup$ Jun 8, 2015 at 4:39
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$\begingroup$ @WetSavannaAnimalakaRodVance the standard model has a Lagrangian. In that Lagrangian the elementary particles are point particles ( in contrast where in string theory they are vibrations on a one dimensional string, for example). Point means (x,y,z,t) in the solutions and is implicit in the very formulation, that is why I call it a postulate. en.wikipedia.org/wiki/Uncertainty_principle . The quantum fields are operators acting on the psi. The psi are defined at (x,y,z,t) $\endgroup$– anna vJun 8, 2015 at 5:52
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$\begingroup$ Hi. May I ask this: If the QM equations-Schrodinger or others give us the probability of finding the particle at some point in space, and if it is this probability distribution that gives us the interference picture, why say that the particle has a wave atribute like an EM field ruther than say it's only it's distribution of probability that gives an interference pattern and not some kind of interference with it's self- it has a posibility of being at certain point in space and each particle could sow up at a point of interference, it's not like it interactes like wave with it's self.? $\endgroup$ Jun 8, 2015 at 8:18
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$\begingroup$ What I mean, and sorry for the long comment, is that the wave nature of a particle isn't quite the same with the wave behaviour of water waves of string waves or EM waves, although it might be the basis of existence of macroscopic waves. Could you ellaborate? Thank you. $\endgroup$ Jun 8, 2015 at 8:20
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$\begingroup$ It is the popularization of the concept that confuses the issue. Even though no physicist is claiming "particle has a wave atribute like an EM field", the electromagnetig wave is a wave in energy distributions of the field. It is only because mathematically the QM equations are wave equations, i.e. have sinusoidal solutions, that the probability is has a wave form. There are a number of physicists trying to find an underlying realist theory whose limit is the quantum mechanical probabilistic behavior. It cannot work because of Lorenz invariance, but that is another story. $\endgroup$– anna vJun 8, 2015 at 8:24
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If you shoot only one photon, you will get only one "spot" (pixel, if your detector is digital). One "spot" does not a pattern make. However, you can predict that there are regions on your detector where the photon will not hit, and no "spot" will appear.
So there is a sense in which the rather poorly defined phrase "a photon interferes with itself" can be understood.
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$\begingroup$ it's a statistical distribution. No region is free of spots. $\endgroup$– user46925Jun 7, 2015 at 22:37
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It seems to me that if shooting one electron does not produce an interference pattern that the conclusion that an electron is spread out everywhere and can be two places at once is wrong. It is also wrong to say that this pattern can only happen after shooting millions of electrons. Shooting million of electrons does not predict the behavior of one electron. It predicts the behavior of millions of electrons. That's like saying that if you switch the electron with many baseballs and perform the same experiment, that because there is a pattern of two marks, that the position of the baseball is spread out everywhere and it can be at two places at once.