The two-slit experiment remains for the most part a thought experiment since it is difficult to build an inexpensive demonstration, but its predictions have been verified in many ways since the 1960's, primarily with electrons. Recently, extremely sensitive CCDs used in photography have been used to collect single-photon events.
The two-slit experiment demonstrates better than any other experiment that a quantum wave function is a probability amplitude
that can interfere with itself, producing places where the probability (the square of the absolute value of the complex probability amplitude) of finding a quantum particle is actually zero.
There is nothing like this in the motion of classical particles, although something like it is well known in the cancellation of crests and troughs in the motion of water and other waves.
The two-slit experiment demonstrates the famous "collapse" of the wave function
or "reduction" of the wave packet, which show an inherent probabilistic element in quantum mechanics that is irreducibly ontological and nothing like the epistemological indeterminacy (human ignorance) in classical statistical physics.
Note that probability, like information
, is neither matter nor energy. When a wave function "collapses" or "goes through both slits" in this dazzling experiment, nothing physical is traveling faster than the speed of light or going through the slits. This is similar to the Einstein-Podolsky-Rosen
experiments, where measurement of one particle transmits nothing physical (matter or energy) to the other "entangled" particle but only the instantaneous information
that has come into the universe. That information, together with conservation of momentum, makes the state of the coherently entangled second particle certain, however far away it might be.
In the two-slit experiment, as in the Dirac Three Polarizers
experiment, the critical case to consider is just one photon at a time in the experiment.
With one photon at a time, we can show the fact that a quantum particle can interfere with itself. Indeed, even in the one-slit case, interference fringes are visible, although this is rarely described in the context of quantum mysteries
It is the two-slit case that raises the "local reality" question raised by Albert Einstein
, Erwin Schrödinger
, and others. How, they ask, can the photon go through both slits? We will see that the thing that goes through both slits is only immaterial information
- the probability amplitude wave function.
Let's look first at the one-slit case. We prepare a slit that is about the same size as the wavelength of the light in order to see the Fraunhofer diffraction effect most clearly. Parallel waves from a distant source fall on the slit from below. The diagram shows that the wave from the left edge of the slit interferes with the one from the right edge. If the slit width is d
and the photon wavelength is λ, at an angle α ≈ λ/2d
there will be destructive interference. At an angle α ≈ λ/d
, there is constructive interference (which shows up as the lightening in the interfering waves in the illustration).
The height of the function or curve on the top of the diagram is proportional to the number of photons falling along the screen. At first they are individual pixels in a CCD or grains in a photographic plate, but over time and very large numbers of photons they appear as the continuous gradients of light in the band below (we represent this intensity as the height of the function).
Now what happens if we add a second slit? Perhaps we should start by showing what happens if we run the experiment with the first slit open for a time, and then with the second slit open for an equal time. In this case, the height of the intensity curve is the sum of the curves for the individual slits.
But that is not the intensity curve we get when the two slits are open at the same time! Instead, we see many new interference fringes with much narrower width angles α ≈ λ/D
, where D
is the distance between the two slits. Note that the overall envelope of the curve is similar to that of one big slit of width D
. And also note many more lightening rays in the overlapping waves.
Remembering that the double-slit interference appears even if only one photon at a time
is incident on the two slits, we have established that the photon interferes with itself.
But how do we see the "collapse" of the wave function
? At the moments just before a photon is detected at the CCD or photographic plate, there is a finite non-zero probability that the photon could be detected anywhere that the modulus (complex conjugate squared) of the probability amplitude wave function has a non-zero value.
If our experiment were physically very large (and it is indeed large compared to the atomic scale), we can say that the finite probability of detecting (potentially
measuring) the photon at position x1
on the screen "collapses" (goes to zero) and reappears as part of the unit probability (certainty) that the photon is at x2
, where it is actually
Since the collapse to zero of the probability at x1
is instantaneous with the measurement at x2
, critics of quantum theory like to say that something traveled faster than the speed of light. This is most clear in the nonlocality and entanglement aspects of the Einstein-Podolsky-Rosen
experiment. But the sum of all the probabilities of measuring anywhere on the screen is not a physical quantity, it is only immaterial information
that "collapses" to a point.
Here is what happens to the probability amplitude wave function (the blue waves) when the photon is detected at the screen (either a photographic plate or CCD) in the second interference fringe to the right (red spot). The probability simply disappears instantly.
The first suggestion of two possible directions leading to interference which disappears if there is only one possible direction was perhaps made by Albert Einstein
at the 1927 Solvay conference on "Electrons and Photons." Niels Bohr
remembered the occasion
In fact, the introduction of any further piece of apparatus, like a mirror,
in the way of a particle might imply new interference effects essentially
influencing the predictions as regards the results to be eventually recorded.
The extent to which renunciation of the visualisation of atomic phenomena
is imposed upon us by the impossibility of their subdivision is strikingly
illustrated by the following example to which Einstein very early called
attention and often has reverted. If a semi-reflecting mirror is placed
in the way of a photon, leaving two possibilities for its direction of
propagation, the photon may either be recorded on one, and only one, of
two photographic plates situated at great distances in the two directions
in question, or else we may, by replacing the plates by mirrors, observe
effects exhibiting an interference between the two reflected wave-trains.
In any attempt of a pictorial representation of the behaviour of the photon
we would, thus, meet with the difficulty: to be obliged to say, on the
one hand, that the photon always chooses one of the two ways and,
on the other hand, that it behaves as if it had passed both ways.
References from Physics World
T Young 1802 On the theory of light and colours (The 1801 Bakerian Lecture) Philosophical Transactions of the Royal Society of London 92 12-48
T Young 1804 Experiments and calculations relative to physical optics (The 1803 Bakerian Lecture) Philosophical Transactions of the Royal Society of London 94 1-16
T Young 1807 A Course of Lectures on Natural Philosophy and the Mechanical Arts (J Johnson, London)
G I Taylor 1909 Interference fringes with feeble light Proceedings of the Cambridge Philosophical Society 15 114-115
P A M Dirac 1958 The Principles of Quantum Mechanics (Oxford University Press) 4th edn p9
R P Feynman, R B Leighton and M Sands 1963 The Feynman Lecture on Physics (Addison-Wesley) vol 3 ch 37 (Quantum behaviour)
A Howie and J E Fowcs Williams (eds) 2002 Interference: 200 years after Thomas Young's discoveries Philosophical Transactions of the Royal Society of London 360 803-1069
R P Crease 2002 The most beautiful experiment Physics World September pp19-20. This article contains the results of Crease's survey for Physics World; the first article about the survey appeared on page 17 of the May 2002 issue.
Electron interference experiments
Visit www.nobel.se/physics/laureates/1937/index.html for details of the Nobel prize awarded to Clinton Davisson and George Thomson
L Marton 1952 Electron interferometer Physical Review 85 1057-1058
L Marton, J Arol Simpson and J A Suddeth 1953 Electron beam interferometer Physical Review 90 490-491
L Marton, J Arol Simpson and J A Suddeth 1954 An electron interferometer Reviews of Scientific Instruments 25 1099-1104
G Möllenstedt and H Düker 1955 Naturwissenschaften 42 41
G Möllenstedt and H Düker 1956 Zeitschrift für Physik 145 377-397
G Möllenstedt and C Jönsson 1959 Zeitschrift für Physik 155 472-474
R G Chambers 1960 Shift of an electron interference pattern by enclosed magnetic flux Physical Review Letters 5 3-5
C Jönsson 1961 Zeitschrift für Physik 161 454-474
C Jönsson 1974 Electron diffraction at multiple slits American Journal of Physics 42 4-11
A P French and E F Taylor 1974 The pedagogically clean, fundamental experiment American Journal of Physics 42 3
P G Merli, G F Missiroli and G Pozzi 1976 On the statistical aspect of electron interference phenomena American Journal of Physics 44 306-7
A Tonomura, J Endo, T Matsuda, T Kawasaki and H Ezawa 1989 Demonstration of single-electron build-up of an interference pattern American Journal of Physics 57 117-120
H Kiesel, A Renz and F Hasselbach 2002 Observation of Hanbury Brown-Twiss anticorrelations for free electrons Nature 418 392-394
Atoms and molecules
O Carnal and J Mlynek 1991 Young's double-slit experiment with atoms: a simple atom interferometer Physical Review Letters 66 2689-2692
D W Keith, C R Ekstrom, Q A Turchette and D E Pritchard 1991 An interferometer for atoms Physical Review Letters 66 2693-2696
M W Noel and C R Stroud Jr 1995 Young's double-slit interferometry within an atom Physical Review Letters 75 1252-1255
M Arndt, O Nairz, J Vos-Andreae, C Keller, G van der Zouw and A Zeilinger 1999 Wave-particle duality of C60 molecules Nature 401 680-682
B Brezger, L Hackermüller, S Uttenthaler, J Petschinka, M Arndt and A Zeilinger 2002 Matter-wave interferometer for large molecules Physical Review Letters 88 100404
Review articles and books
G F Missiroli, G Pozzi and U Valdrè 1981 Electron interferometry and interference electron microscopy Journal of Physics E 14 649-671. This review covers early work on electron interferometry by groups in Bologna, Toulouse, Tübingen and elsewhere.
A Zeilinger, R Gähler, C G Shull, W Treimer and W Mampe 1988 Single- and double-slit diffraction of neutrons Reviews of Modern Physics 60 1067-1073
A Tonomura 1993 Electron Holography (Springer-Verlag, Berlin/New York)
H Rauch and S A Werner 2000 Neutron Interferometry: Lessons in Experimental Quantum Mechanics (Oxford Science Publications)