Triple-slit experiment tests the Born's rule


by giann_tee
Tags: born, experiment, rule, tests, tripleslit
giann_tee
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Jul24-10, 08:44 AM
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A simple experiment that sends photons through three slits provides the best proof yet of an important axiom of quantum theory called Born's rule, say physicists in Canada and Austria. The confirmation also provides important guidance to those seeking the holy grail of physics – a quantum theory that includes gravity.
http://physicsworld.com/cws/article/news/43275

...and in another famous magazine:
http://www.physorg.com/news199009831.html

Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification. For example, Born’s rule—one of the axioms of quantum mechanics—could be violated. Born’s rule predicts that quantum interference, as shown by a double-slit diffraction experiment, occurs from pairs of paths. A generalized version of quantum mechanics might allow multipath (i.e., higher-order) interference, thus leading to a deviation from the theory. We performed a three-slit experiment with photons and bounded the magnitude of three-path interference to less than 10–2 of the expected two-path interference, thus ruling out third- and higher-order interference and providing a bound on the accuracy of Born’s rule. Our experiment is consistent with the postulate both in semiclassical and quantum regimes.
http://www.sciencemag.org/cgi/conten...t/329/5990/418

In Mod. Phys. Lett. A 9, 3119 (1994), one of us (R.D.S) investigated a formulation of quantum mechanics as a generalized measure theory. Quantum mechanics computes probabilities from the absolute squares of complex amplitudes, and the resulting interference violates the (Kolmogorov) sum rule expressing the additivity of probabilities of mutually exclusive events. However, there is a higher order sum rule that quantum mechanics does obey, involving the probabilities of three mutually exclusive possibilities. We could imagine a yet more general theory by assuming that it violates the next higher sum rule. In this paper, we report results from an ongoing experiment that sets out to test the validity of this second sum rule by measuring the interference patterns produced by three slits and all the possible combinations of those slits being open or closed. We use attenuated laser light combined with single photon counting to confirm the particle character of the measured light.
http://arxiv.org/abs/0811.2068
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ZapperZ
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Jul24-10, 09:03 AM
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You might want to check the Recent Noteworthy Paper thread in the General Physics forum.

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giann_tee
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Jul24-10, 09:13 AM
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http://www.physicsforums.com/showthr...=127314&page=8

I see. It seems a little bit cramped thread for a reply?

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Jul24-10, 09:34 AM
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Triple-slit experiment tests the Born's rule


That thread isn't meant for having a discussion. I only pointed it out so that (i) you know it exists and (ii) that it can be used as a source for a discussion in another thread.

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giann_tee
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Jul24-10, 09:15 PM
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After reading the article at http://arxiv.org/abs/0811.2068, I came to certain ideas about the physics of probability waves.

The holes behave as three point-like light sources. The three-wave interferential pattern must exist on large scales in the universal case, but it does not in this experiment on micron scales and with the coherent light.

Note: Some portion of space is covered with shadows made by the walls between the holes, given a single underlying source behind the holes. The shadows are rarely mentioned or non-existent in similar experiments.

Maybe its not the scale that matters the most. The interference depends from the quantum coherence: after a single interaction, the photons decohere.

While the light from the laser remains coherent after the diffraction and interference, after the first interaction, such as the one that would determine which hole the photon went through, it would lose its magic that allows it to go through both holes statistically speaking.

www.answers.com…quantum-decoherence

One particle is a statistical (quantum) ensemble. It can go through either of the two holes with the probabilities p1, p2, until we actually determine the hole through which it went by interacting with the particle at that hole. The probabilities are a wave-like physical property.

All particles are not waves, and waves are not waves because as they are quantized, they hit the film one by one and imprint dots. If they were just waves, any single wave would produce the entire interferential pattern at once each time it went through a large number of holes (the size of which is comparable to its wavelength).

This points out that the light is sometimes more or less suitable for interference. The question is whether the rules that determine the possibility of interference are more complex than my explanation based on decohering (in a single sentence). That is where the Born's rule comes in.

http://www.answers.com/topic/double-slit-experiment

We are sending single, sparse photons and the expectation is that there is a single interaction between the coherent wavepackets. The two wavepackets are two photons, or perhaps a single photon interacting with itself, as suggested in numerous previous works interpreting the double-slit experiment. The sparse, single photons appear to fly at random times in slightly different, random directions from the source. Presumably, they are still adequately coherent on average for the interference.

On the borderline with madness, a single source photon interacting with itself could represent a perfect, singular source of the coherent beam. This case creates a self-amplifying photon in some portions of the space, unless its energy is kept constant by setting the result of the constructive self-interference to its existing amplitude.

The photons or other particles enter a grid of any kind of holes from where they emerge as interacting "beams". The beams are narrow because they possess the particle-like properties. The interferential pattern appears cumulatively, solely by particle number count per unit area per unit of time.

There is not any interaction of light with the holes or at least it is not spoiling the result, the virginity of the statistical ensemble before the first interaction. That is an odd conclusion given that the ordinary waves passing through ordinary holes bend at (after) the holes, approximately speaking; later, they interfere. The explanation for the fringe development is in any case the extinction by interference of particles at certain pathways taken out of the statistical set of all the initial directions. If holes change the direction of wavepackets, then they do so by respecting their particle nature.

A material such as the diffraction grating is likely absorbing the extra light and converting it into heat.

The interesting moments for further discussion are the shape of a wavepacket, the interaction of wavepackets with matter and the mutual interactions of wavepackets.

For example, when an electron beam interacts with the diffraction grating, we expect many electrons to pass at once through the holes to mutually interact. However, single, sparse electrons do not seem to have any companions during the flight to drive them in the direction (and speed) at which they will hit the film.

One could propose that the electrons (or photons) have invisible companions that appear after the diffraction grating. Some propose that the electron wavepacket cannot break apart at the entrance to a hole, but that its wavefunction consisting of the probabilities p1, p2… can. Other suggestions include the interaction with the matter. As the particle is passing through the grid of holes, it only needs to interact with a long-gone particle that passed the similar journey. How? I would say by interacting with the trace memory contained in the diffraction grating.

Another possibility is to revise the idea of the field as the space that contains the beam of light or electrons. Even though the photon’s energy is concentrated in the photon loosely speaking, the neighborhood of its path contains the physical probability wave as a non-energetic component that does contain information sufficient to define the interference of a single photon after diffracting through two holes.

I wonder if the Born’s rule actually talks about the magic of the statistical ensemble and when it is lost. If that happens after the first interference (as the magic is lost at the first interaction in other experiments), then the triple-slit experiment truly walks along the crucial edges of the quantum phenomena. This is why we should give in to learning more about these details of the quantum mechanics.
giann_tee
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Jul25-10, 11:28 AM
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Simple interference with a green laser pointer through different number of slits...

Under the Fraunhofer conditions, the light curve of a multiple slit arrangement will be the interference pattern multiplied by the single slit diffraction envelope. This assumes that all the slits are identical.
http://hyperphysics.phy-astr.gsu.edu...ulslid.html#c3
giann_tee
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Jul27-10, 05:17 PM
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The article http://arxiv.org/abs/0811.2068 mentions that the "quantum measure" is a more general type of statistics than the classical one. If we consider the two slits with probabilities p_A, p_B of a particle going through, the classical picture demands exclusively one or the other event to occur. The quantum physics recognizes both slits as a contending option for the passage of a single particle.

The three-slit experiment
Imagine an experiment in which an electron (say) passes through any one of three slits and impinges on an array of detectors. Imagine that you record the diffraction pattern with all three slits open, and then repeat the procedure with some of the slits blocked off. In all, you can obtain in this way a total of eight diffraction patterns. Now superimpose the eight patterns, using a plus sign when an odd number (3 or 1) of the slits were open, and a minus sign when an even number (2 or 0) were open. What will be the result? Remarkably, you will always get zero, as can be straightforwardly demonstrated. Were the electron a classical particle, you would also get zero, since each of the three slits would contribute twice with a positive sign and twice with a negative one. In this sense, quantum randomness preserves something of the classical additivity of probabilities. One can go further and imagine diffraction experiments with four or more slits. For each case beyond two slits the analogous superposition will again yield zero, but it turns out that these subsequent relations yield nothing new, each of them being logically contained in the three slit relation. I will describe this hierarchy of sumrules more carefully below, but first I want to sketch the interpretive framework in which I would propose to situate them.
http://arxiv.org/PS_cache/gr-qc/pdf/9401/9401003v2.pdf at the page two.

The above logic is illustrated on the page ten of the following article. Here's a brief quote somewhat out of context...

A striking illustration of this difficulty is furnished by the three-slit experiment referred to earlier, which we may idealize for present purposes as a source emitting spinless particles which impinge on a diffraction grating with three slits. (See figure 2.) Let P be a spacetime region—idealized as a point—which is aligned with the central slit and consequently sits within a “bright band” of the diffraction pattern. For such a point, the rule (1) yields a nonzero value for the measure |{1, 2, 3}| of the set of all world lines that arrive at P via any one of the slits, and we know, in fact, that if we look for the particle at P by placing a detector there, we will often find it. On the other hand, we can choose the separation between the slits so that, when taken in pairs {1, 2} or {2, 3}, the amplitudes cancel, and correspondingly, the measures of E = {1, 2} and of F = {2, 3} will vanish: |E| = |F| = 0. An unrestricted preclusion rule would then entail that the actual history could belong neither to E nor to F, whence it could not arrive at P at all—a false prediction. More generally, one can typically embed any given history γ in a subset S ⊆ H of zero measure, whence every possibility without exception would be ruled out by an unrestricted preclusion rule...
http://arxiv.org/PS_cache/gr-qc/pdf/9507/9507057v2.pdf at the page ten.
giann_tee
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#8
Sep2-10, 09:04 AM
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I discovered that reading about the quantum superposition is quite a treat. It is good for training the insight into the quantum probabilities.

http://www.answers.com/topic/quantum-superposition
giann_tee
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Sep2-10, 09:07 AM
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A theory on the origin of quantum probabilities, Born principle and the rest.

Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some features with quantum theory, such as probabilistic predictions for individual outcomes (indeterminism), the impossibility of information transfer faster than speed of light (no-signaling) or the impossibility of copying of unknown states (no-cloning). A vast majority of attempts to find physical principles behind quantum theory either fall short of deriving the theory uniquely from the principles or are based on abstract mathematical assumptions that require themselves a more conclusive physical motivation. Here, we show that classical probability theory and quantum theory can be reconstructed from three reasonable axioms: (1) (Information capacity) All systems with information carrying capacity of one bit are equivalent. (2) (Locality) The state of a composite system is completely determined by measurements on its subsystems. (3) (Reversibility) Between any two pure states there exists a reversible transformation. If one requires the transformation from the last axiom to be continuous, one separates quantum theory from the classical probabilistic one. A remarkable result following from our reconstruction is that no probability theory other than quantum theory can exhibit entanglement without contradicting one or more axioms.
http://arxiv.org/abs/0911.0695
giann_tee
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Sep2-10, 09:11 AM
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As a side note to this topic I would like to add the recent article from New Scientist. It deals with how great discrepancy is between the quantum mechanics and the cosmological measurements. (Some of the authors of the triple-slit experiments said that they aim towards unifying the QM and general relativity.)

The vacuum energy compared to the cosmological constant:

http://www.newscientist.com/article/...gy-puzzle.html

QCD estimate of the quark-gluon condensate's energy density: 10^45 times the cosmological constant that we measure from observations of the universe's expansion.

The Higgs boson, thought to be partially responsible for giving other particles mass, has an associated field whose vacuum energy is 10^56 times the observed cosmological constant. Meanwhile, the vacuum energy associated with grand unified theories that aim to unify electromagnetism and the nuclear forces gives a value 10^110 times too big.

The biggest disparity of all comes from attempts to unify quantum mechanics and general relativity. Under so-called quantum gravity, the energy density is 10^120 times too big.
ZapperZ
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Sep2-10, 11:14 AM
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Quote Quote by giann_tee View Post
A theory on the origin of quantum probabilities, Born principle and the rest.



http://arxiv.org/abs/0911.0695
Please note that we strongly recommend that you only used sources that have been published in peer-reviewed journals. If you know where this preprint has been published, please make a full citation to it. If not, then I would suggest you wait until it has been published before putting time and effort into studying it. The same goes when you cite stories appearing in popular magazines such as New Scientist and SciAm.

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giann_tee
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Sep2-10, 01:46 PM
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Quote Quote by ZapperZ View Post
Please note that we strongly recommend that you only used sources that have been published in peer-reviewed journals. If you know where this preprint has been published, please make a full citation to it. If not, then I would suggest you wait until it has been published before putting time and effort into studying it. The same goes when you cite stories appearing in popular magazines such as New Scientist and SciAm.

Zz.
I did not know that arXiv was ... nutty! There was a story behind the story in New Scientist, but they hide the article after a period for non-subscribers. I prepared the link to the article at arXiv, because otherwise we would be completely without access.
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Sep3-10, 07:36 AM
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Quote Quote by giann_tee View Post
I did not know that arXiv was ... nutty! There was a story behind the story in New Scientist, but they hide the article after a period for non-subscribers. I prepared the link to the article at arXiv, because otherwise we would be completely without access.
I didn't say arXiv was nutty. That would be silly since even I have uploaded my manuscripts there. I said "peer-reviewed".

arXiv doesn't require a manuscript to have been peer-reviewed. This allows for some "professionals" who have fringe ideas to post there, since that is the only place where such a thing can see a light of day. You will be wasting time and effort if you're dissecting and studying a manuscript that never made it into any kinds of journals, and that others pay little attention to. There are so many other important papers that are worth our time, so it is hard to understand why we have to dig the very bottom of the barrel.

The other important aspect of peer-reviewed publications is that it allows for many of us to do a citation index lookup. A paper that is published, if it is worth anything, will get cited. In such a citation, we can see how many other independent publication agrees or disagrees with that paper. Just because something appears in a journal does not make it valid. Knowing what the experts in that same field thinks about a publication is important. This is all part of what something has to go through to be considered to be valid. If it isn't published, there is very little to go on.

While the field of high energy physics and string theory have a common practice of using arXiv manuscripts as sources, the rest of physics still very much rely on peer-reviewed journals. The manuscript you cited appeared on arXiv a few years ago. I can't find where it was published. If it hasn't, then all the warning bells should go off here on why it can't make it into the many different tiers of physics journals that are available.

Zz.
unusualname
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Sep3-10, 02:19 PM
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This experiment just confirms that we can add the individual probability amplitudes to get the total interference.

That's nice to know, but it was hardly unexpected and I don't see why gian_tee is developing the thread into a blog about all sorts of speculative and hardly related issues.

What they rule out is the possibility that when more than two paths are available you don't need to consider any higher order contributions to the interference pattern than those obtained from summing the individual probability amplitudes, which is exactly what QM predicts.

I'm not sure why the article in physicsworld suggests that this is helpful for people working on Quantum Gravity, I don't think anyone doubted the correctness of the Born rule, but it's nice to know there is additional experimental verification.


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