<html> <head> <title>Albert van der Sel : Intro Interpretations in Quantum Mechanics</title> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> </head> <body> <h1>A few notes on Entanglement, Decoherence, and other aspects of Quantum Mechanics (QM).</h1> Version : 0.8 <br> Date : 25/01/2012<br> By : Albert van der Sel<br> Type of doc : Just an attempt to decribe the subject in a few simple words. Hopefully, it's any good.<br> For who : For anyone interested. <br> <hr/> <br> The sole purpose of this doc, is to quickly introduce some concepts, that hopefully "clarifies"<br> a few important concepts like "entanglement", "decoherence", "MWI", "PWI", and interpretations of QM in general.<br> <br> <font face="arial" size=2 color="blue"> Contents:<br> <br> 1. A few words on "entanglement<br> 2. A few words on "non-locality"<br> 3. A few words on (classical) "Copenhagen interpretation"<br> 4. A few words on "Decoherence"<br> 5. A few words on Everett's "Many Worlds" Interpretation (MWI)<br> 6. A few words on Porier's "Waveless" Classical Interpretation<br> 7. A few words on de Broglie - Bohm "Pilot Wave" Interpretation (PWI)<br> 8. A few words on Weak Measurements and TSVF<br> <font face="arial" size=2 color="black"> <br> <br> <font face="arial" size=2 color="blue"> <h3>1. A few words on "entanglement":</h3> <font face="arial" size=2 color="black"> Probably the discussion in this section is a bit too "Copenhagen-style" oriented, but that is how entanglement<br> usually is introduced, in most literature.<br> <br> Erwin Schrdinger came up with the expression  entanglement , and called it <I> the"</I> characteristic trait of quantum mechanics.<br> <br> Many of us probably have heard of it, but often it is felt as a rather "strange" effect.<br> <br> Indeed, what is it ? Let's consider a two "particles" system. In a special case, their common state can be in such a way,<br> that we may only describe it effectively as being two parts of <I>the same entity</I>.<br> Like the word "entanglement" already suggests, it's a sort of "correlation". In better words:<br> you need both particles in order to fully 'describe' the state of the system.<br> <br> Fig 1.<br> <img src="entanglement1.jpg" align="centre"/> <br> The &Psi;(r,t) function of a single particle in QM, describes the system as a distribution in space (r) and time (t).<br> When you would consider a two particle system, the state of the two-particle system would described by the wave function &Psi;(r1,r2,t). <br> <br> If we would leave out time for a moment, and if the particle one is in &Psi;A(r) state and particle two is in &Psi;B(r) state,<br> then the total state can be written as the product &Psi;(r1,r2)=&Psi;A(r1) . &Psi;B(r2)<br> <br> But the "expression" as shown in figure 1, is quite different. Here it is not possible to seperate the entangled state<br> into product states.<br> <br> In figure 1, you see up and down arrows. This is so, because in this example, we are looking at a special property<br> that a particle might have, which is called 'spin", which can be thought of as some sort of "angular momentum".<br> Note that many articles use entangled photons, where the "polarization" is used in a similar sense.<br> <br> Take a look at this expression again:<br> <br> <font face="arial" size=3 color="black"> <B>&Psi;a,b=1 / &#8730; 2 ( |&#8593; &#8595;> + |&#8595; &#8593;> ) </B><br> <font face="arial" size=2 color="black"> <br> Now please notice this: It's a <B>quantum superposition</B> of two states, namely <B> &#8593; &#8595; </B> and <B> &#8595; &#8593; </B>,<br> which we might call "state 1" and "state 2". In such a state, as for example | &#8593; &#8595; ><br> we see particle A as &#8593; and particle B as &#8595; <br> <br> In state 1, Particle A has spin along +z and particle B has spin along -z. <br> <br> In state 2, Particle A has spin along -z and particle B has spin along +z. <br> <br> (here in this example, we look with respect to the z direction; but any other direction could have been choosen)<br> <br> Now suppose the particles are moving in opposite directions.<br> <br> Alice has placed a detector where particle A will fly by, and Bob did the same at where particle B goes to.<br> Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or -z. <br> <br> Suppose she gets +z. According to what <B>we know of the collapse of the wave function</B>, the quantum state of the system <br> will collapse into state 1.<br> Thus Bob then will measure -z. Similarly, if Alice measures -z, Bob for sure will get +z.<br> No matter what the distance between Alice and Bob is.<br> <br> Isn't that amazing? If Alice gets +z, Bob gets -z, and the other way around. How do both particles know that?<br> I mean: the entangled system is in a superposition of |&#8593; &#8595;> and |&#8595; &#8593;>.<br> Especially when the distance between particle A and particle B is large, it's quite puzzling.<br> However, most physicist don't believe that a superluminal (faster than light) signalling operation is at work here.<br> But what is it then?<br> <br> First I have to admit that in the example above, I oversimplified matters. In experiments, in fact statistical results<br> are obtained, using many entangled particle systems. Due to various reasons, not only the spin along z is measured, but also along<br> the x (or y) direction. Finally, the results are tested agains te socalled "Bell" (or derived) inequalities.<br> But.. currently, all results seem to sustain the conclusion of the example presented above.<br> <br> Many "suggestions" have been forwarden, like "hidden variables" (which we don't know of yet), which works in such way<br> so that from the start of entanglement, a sort of hidden "contract" can explain the oserved effects.<br> But many other "explanations" go around too, like Multiple Universes (MWI), or some still <I>do</I> believe that a "spooky action"<br> that exceeds the speed of light is at work, or that our interpretation of space-time isn't correct etc.. etc..<br> However, many physicists say that the observed results happen with "probabilities" and this type of correlation<br> does not automatically imply communication.<br> Indeed, most physicist accept that non-locality effects of this sort, is simply "non-signalling".<br> <br> Note that a key point is, that the entangled system is in a superpostion (thus both simultaneously) of two states <B> &#8593; &#8595; </B> and <B> &#8595; &#8593;</B>.<br> According to the Copenhagen interpretation, when a measurement is done, the system "collapses" into <B>one</B> state.<br> A puzzling element still remains, that a superpostion of states exists, no matter how far the particles are apart. But when<br> for example particle A is measured as &#8593; , then B will be &#8595;.<br> So, what is the meaning of the original superposition?<br> <br> <br> <font face="arial" size=2 color="blue"> <h3>2. A few words on "non-locality":</h3> <font face="arial" size=2 color="black"> Now, intuitively, if particle a and particle b are really close together, we might not be too disturbed, if on the left,<br> we measure "up", and on the right we measure "down" (or vice versa), although it doesn't feel right acording to the superposition<br> principle of substates, as expressed in QM.<br> <br> But now, suppose that the detectors "left" and "right" are really quite far apart, and if we then still observe the same<br> results, it might get more puzzling.<br> <br> Suppose partice a is found to be "up". Now suppose particle "a" has a nifty "means" to inform "b", that it was measured as "up", and thus<br> "b" now knows that it has to be "down". Now suppose that really such a fantastic mechanism would exist.<br> But there is a problem if the distance between "a" and "b" is so great, that "a" would have to use a mechanism that exceeds the<br> speed of light.<br> Indeed, certain experiments suggests that the correlation still remains, even if there is no way that "a" can inform "b", or "b"<br> can inform "a", how it was measured, unless a superluminous signalling mechanism would be at work.<br> Clearly, that is not generally acceptable, since it conflicts with Special Relativity Theory of Einstein.<br> Also, this is what Einstein called "the spooky action at a distance".<br> <br> You know, there are many "interpretations" out there, to explain the effect. <br> When you would believe in <B>"Local reality"</B>, you would say the <B>state</B> of an observable<br> would be clearly defined. Now, you could <I>measure</I> some observable and obtain a certain result.<br> It's quite accepted, that when you measure some observable, in many cases you would interact with that system, <br> and thus you would have exterted some influence on that system.<br> It's "pretty close" to what the idea of "local realism" actually is, but not entirely.<br> Local realism is somewhat opposed to what QM seems to "look like": <B>QM is probabilistic in nature.</B><br> If you would favour the idea of local realism, you probably would not like QM too much, and you might argue that<br> QM can't be a full and complete theory.<br> <br> The essential meaning of Local realism then would be, that a system truly has some defined state, and is not "fuzzy" at all.<br> Even if it would just "appear" to be probabilistic (fuzzy), then below the surface, something like "hidden variables"<br> are at work, (which we don't know about, yet) which would make it "exact".<br> <br> The "hidden variables" would then also be the mechanism to explain the seemingly non-local effect, as we have seen at those<br> two particles, seperated over a long distance.<br> <br> However, most physicists accept that "non-locality" is a fundamental aspect of Nature.<br> Some scientists have come up with some other very interesting arguments. In effect they say:<br> We are used to the fact that <B>space</B> and <B>time</B> are our defining "metrics" to valuate experimental results.<br> But (as they say), quantum non-locality shows us that there has to be more, something that we are just not sure about yet.<br> <br> There are some ideas though, on the "new" structure of space and time, to explain nonlocality.<br> One idea is the concept of "prespace". Partly based on original ideas of Bohm, Hiley (and others) formulated the concept<br> of "prespace", which essentially says that the "usual" space-time manifold emerges from a more fundamental level of physical space.<br> Using a "Quantum Potential" and a new revised idea of "time", they formulated a framework which might explain nonlocality.<br> <br> Another great way to theoretically analyze entanglement, is the EPR wormhole.<br> Some (theoretical) physicists, are working on models that associate the smallest<br> space-time building blocks, with socalled ER=EPR Plank-scale "wormholes". In many cases, they focus especially<br> on the Quantum Mechanical effect of "entanglement", and believe it or not, some articles make sense how such planck scale<br> wormholes connect entangled particles. However, many physicists are sceptical, and like much more "body" on those models.<br> <br> <br> <font face="arial" size=2 color="blue"> <h3>3. A few words on the (classical) "Copenhagen interpretation"</h3> <font face="arial" size=2 color="black"> The measurement of an "observable" of a system like a particle, can be described in several ways.<br> One method which "seems" to be quite natural in QM, is to to describe the system as a superposition of "eigenfunctions",<br> just like you can describe a vector in n-space as being composed of n orthogonal eigenvectors.<br> (Note: Below is a very simple example of a socalled a "bra" "ket", that is,"|>" equation.)<br> <br> Fig 2.<br> <br> <img src="qm1.jpg" align="centre"/> <br> In this way, it's also described, what the "probabilities" of the possible values of the observable could be.<br> These probabilities are namely <I>related</I> to the <I>coefficients</I> of the above equation.<br> <br> So, let's suppose that some sort of "measurering apparatus" finds value "c3", then at least one important question arises.<br> Why did the system collapsed into the state c3|3>, and what happened to all the other eingenstates?<br> <br> This is an example of the socalled "collapse of the wavefunction". If an actual measurements is done,<br> out of many possible results, just one is "selected" in "some way"<br> An observable, initially in a superposition of different eigenstates, appears to reduce to a single value<br> of the states, after interaction with an observer (that is: if it's being measured).<br> <br> It has puzzled many people for years, and different interpretations have emerged.<br> Although "Quantum decoherence" (more on that later) is quite accepted by most folks nowadays,<br> other interpretations exist as well.<br> <br> The so-called "Copenhagen" interpretation, accepts the wavefunction (or state vector) as a <I>workable</I> solution,<br> and the collapse that happens at a measurement, is a way to describe why a particular value is selected.<br> As a simple example, they would say that a system can for example be described as &Psi; = a|1> + b|2>,<br> and we have probability |a| to find the observable to be in state |1>.<br> <br> So, it says that a quantum system, before measurement, doesn't exist in one state or another,<br> but in all of its possible states at once.<br> <br> The "Copenhagen" interpretation is most often "associated" with the principle of the <B>"collapse of the wave function"</B>,<br> when a measuerment is done. But it does not strictly mean that all who favour this description,<br> also believe in the physical reality.<br> <br> Bohr seemed to have gone one step further (in a later phase), by essentially saying that the wavefunction<br> is not equal to a "true" <B>pictorial</B> description of reality, but instead is (just) a symbolic representation.<br> <br> With a litle "bending and twisting", you might call this view and methodology, something like the "early"<br> cornerstone of QM. The theory is succesfully applied at many physical systems.<br> For example at the Hydrogen atom, any eigenstate of the electron in the hydrogen atom is described fully<br> by a number of quantum numbers. Also, the actual state of the electron may be any superposition of eigen states.<br> <br> However, important insights which differ greatly from the "Copenhagen" interpretation, surfaced more or less at<br> the same time. An important one is the "deterministic" and realistic <B>Hidden variables</B> Quantum framework,<br> and ofcourse the <B>Pilot Wave</B> interpretation developed by de Broglie around 1927 and further refined<br> by Bohm around 1952.<br> <br> In the Copenhagen interpretation, the wavefunction is a superposition of eigenstates. In slightly different words:<br> It says that a quantum system doesn't exist in one state or another, but in all of its possible states at once.<br> A very simple example is this: &Psi; = a|1> + b|2><br> It's only when we observe its state, that a quantum system is forced to choose one "probability", and collapse<br> into a certain eigenstate (which produces a certain value for an observable)<br> So, When we observe an object, the superposition collapses and the system is forced into <B>one of the states</B><br> of its wave function.<br> <br> In figure 3, you see a few other examples of "superposition", and ways to denote the wavefunction:<br> <br> Fig 3.<br> <br> <img src="entanglement2.jpg" align="centre"/> <br> Many people have disliked the postulate of a wavefunction that collapses, without a associated physical reality, as was<br> implied by the Copenhagen Interpretation.<br> <br> One philosophical question is this: How and why does the unique world of our experience, at measurement, then emerge<br> from the multiplicities of <B>all alternatives</B> available in the superposed quantum world?<br> Also, as said before, the Copenhagen interpretation states that a quantum system, before measurement,<br> doesn't exist in one state or another, but in all of its possible states at once.<br> <br> One classical "thought experiment" tries to illustrate the shortcomings of the Copenhagen interpretation.<br> It's the famous "Schrodinger Cat" thought experiment.<br> <br> <B><U>Schrodingers Cat:</U></B><br> <br> When taken literaly, and to the extreme, a nice (and famous) paradox can be constructed. Suppose a cat is trapped<br> inside a completely sealed box. Inside the box, a radioactive source is present with a certain QM probability to decay.<br> If that happens, some mechanisme activates, and it releases a deadly poison, that will kill the cat immediately.<br> Now consider an external observer, who does not know the state of the cat.<br> Under the Copenhagen description, the observer whould describe the cat as: <B>|state of cat> = a|alive> + b|dead></B>.<br> Only when a "measurement" is done, that is, the observer opens the trap and checks the state of the cat, that state<br> would collapse to either "dead" or "alive". This is ofcourse somewhat absurd.<br> <br> Now, this "macroscopic" example, is really not quite comparable to the microscopic world where QM seems to dominate.<br> The point seems to be, that the paradox nicely illustrates how hard it is to deal with the description<br> of a superposition of states, and the collapse of the wavefunction.<br> <br> Among other interpretations, three other important interpretations emerged.<br> <br> <ul> <li>The <B>"Many Worlds Interpretation (MWI)"</B> dates from 1957.<br> This theory, although it's quite consistent, never had <I>too</I> many supporters (at that time).<br> By a Quantum event, where we formerly would say in the Copenhagen language, that the superposition collapes into<br> an eigenstate with a certain probability, in MWI it is proposed that the World forkes into different Worlds<br> in accordance to the number of superimposed subwaves which all could have been observed.<br> Hence, Many Worlds come into existence, and all different parallel Worlds will evolve independently.<br> <li>The other one, <B>"Decoherence"</B> stems from around 1980-1990 (or so), and received quite much acceptance in the physics community.<br> It mainly provides for an explanation of the strange "collapse" of the statevector.<br> Roughly, it says that due to the interaction of the Quantum System with the environment (or measuring device)<br> only selected components of the wavefunction are decoupled from a coherent system, and are "leaked" out<br> into the environment.Ultimately, we will measure only one component of such selection.</li> <li>The <B>"Pilot Wave Interpretation (PWI)"</B> was developed by de Broglie in 1927, and work was continued by Bohm in 1952.<br> It's an almost classical interpretation. A real particle, is guided by a distributed "guiding" wave.<br> If you see this theory in scientific articles, then you would appreciate the fact that quite a few paradoxes are "solved"<br> (like the wave-particle paradox), as many see it.</li> </ul> <br> The first two above still use the "state vector" or "wave function" as proposed Schrodinger, Bohr and others.<br> but the interaction with the environment, and measurement process is quite different from that of the collapse<br> used in the Copenhagen interpretation.<br> <br> The <B>"Pilot Wave Interpretation"</B> uses real localized objects, with a complex Pilot wave, which shifts all "wavy" stuff<br> to the Pilot wave itself.<br> <br> A very recent interpretation eliminates the wave function all together. Around 2012, an interesting model was established<br> by Bill Poirier. Here the "wavy" stuff and associated probabilities, is an illusion due to the fact that classical<br> parallel universes exist, where in each of them, the Quantum System has clear defined values.<br> It simply just depend in which universe the observer interacts with the Quantum System.<br> <br> Below you will find sections which briefly will touch those different interpretations.<br> <br> <br> <font face="arial" size=2 color="blue"> <h3>4. A few words on "Decoherence":</h3> <font face="arial" size=2 color="black"> This rather new interpretation, has it's origins in 1980s and 1990s. In a sense, this theory "de-mystifies" certain<br> formerly unsolved mysteries, for example, why and how a quantum system interacts with the "environment", and<br> the "measuring device".<br> Also, the Copenhagen phrase "Collapse of the wavfunction" is replaced by quite a solid theoretical framework.<br> <br> Many physicists have embraced the theory, and it seems that only a minority of sceptics remain.<br> Especially technical and experimental oriented physicst, for example working on the field Quantum Computing,<br> see the theory as one of their primary working tools.<br> (For example, sometimes they want to preserve a qubit or nqubit for some time, <I>before it de-coheres</I>).<br> <br> However, in general, we all must be carefull in associating "truth" to any theory at all. It's just characteristic<br> of science, that theories ever evolve, and once in a while, even get completely replaced by better ones.<br> But the "decoherence" framework, is might well be, the best interpretation of QM we have right now.<br> <br> Decoherence is important in the area of "the measurement problem", possibly also to "the flow of time", and<br> above all it's very appealing for most physicists because it seems to solve the question on how the "classical world"<br> emerges from quantum mechanics.<br> <br> Key to the "Decoherence" interpretation, is that it was realized that the "environment" and the quantum system (like a particle)<br> are really tied into a temporary "entangled" system, for a certain duration.<br> Ofcourse, it was already long known that a measurement will influence any system, but this time, a whole framework<br> emerged from "the deep intertwinement" of the quantum system and the environment.<br> <br> In a nutshell, the central idea of the theory goes (more or less) like this:<br> <br> As usual, initially, an undisturbed quantum system, is a superposition of coherent states.<br> When the quantum system and the environment (the environment as a whole, or a measuring device) starts<br> to interact, the coherent states will <B>"decohere"</B> into socalled "pointerstates" which are really<br> determined by the environment. It means the loss of coherence or ordering of the phase angles between the components<br> of the quantum superposition. Effectively, the Copenhagen "phrase" <I>"collapse of the state vector"</I>,<br> this time has a real physical basis or "explanation".<br> After the system has decohered, these "pointerstates" corresponds to the eigenstates of the observables.<br> In other words, only selected components of the wavefunction are decoupled from a coherent system, and are "leaked" out<br> into the environment.<br> This selection of pointerstates is also called "einselection" in various articles describing decoherence.<br> <br> Again rephrased in slightly other words: the wavefuctions of the environment and the quantum system, will interact<br> in such a way, that the coherent superposition of the quantum system will <B>de-cohere</B> and "ein-selected" states<br> remain, which resembles a classical system again.<br> This too is quite important: before the decoherence phase, the system is truly a Quantum sytem, that is, a superposition.<br> Then, after the "perturbation", or de-coherence phase, the system behaves much like a classical system.<br> So, for the first time, a clear boundary has emerged between a pure Quantum state, and what is believed to be "classical".<br> <br> Note that the theory provides for a better explanation for what happens at a measurement, or interaction,<br> with the environment, compared to the Copenhagen interpretation.<br> <br> For example, do you notice that "Quantum decoherence" only gives the <B>appearance</B><br> of wave function collapse?<br> <br> In the interpretation using the principle of "decoherence", is not possible to separate an object being measured,<br> from the apparatus performing the measurement. Or, to seperate the object from the "environment".<br> In this interpretation, in any interaction between the system and the environment, decoherence takes place,<br> and not just when you use some measurement device. <br> Generally speaking, the environment and the particle are bound, or entangled, in such a way, that only a subset <br> of superimposed waves (the "pointerstates) is "selected". <br> After the de-coherence phase, the actual value of an observable is selected from the pointerstates.<br> <br> This new interpretation has quite some philosophical impact as well. The theory further describes how the environment<br> sort of "monitors" the de-cohered systems, and it affects our human perception as well.<br> There is a sort of redundancy of the pointer states in the environment, simply because there is "a lot" of environment<br> out there. So to speak, the environment "bans" arbitrary quantum superpositions.<br> Once a system has decohered, and only pointerstates remain (determined by the environment), and we as observers<br> come on the second place. The environment "observes" the system, and determines what "we get to see" from the system.<br> Ofcourse, any apparatus is part of the environment too, so it makes sense.<br> <br> What might be nice to notice, is that the "decoherence" theory implies that the quantum wavefunction is a physical reality<br> rather than a mere abstraction, or postulate, as in many other interpretations.<br> <br> <B><U>Non-locality and Decoherence:</U></B><br> <br> Nonlocality is hardly seen at macroscopic level because of "hard" decoherence, caused by so many interactions<br> with the environment.<br> But what happens with two entangled microscopic particles, flying away in different directions, and keeping their "correlation"?<br> In section 2, we touched on that subject. First of all, non-locality still seems to be a fundamental feature of QM.<br> Non-locality is ofcourse more than just the example of the two entangled particles of section 2.<br> However, it's still a "strong" example of nonlocality, that is, the absence of a local agent (see section 2).<br> <br> But decoherence is a "powerfull mechanism" to destroy quantum features, so what about "non-locality"?<br> It's not easy to answer this one. Much experimental work, and theoretical studies have been done, and it's<br> probably fair to say that a <B>very conclusive</B> answer is not reached yet.<br> At first sight, decoherence might look like a local mechanism (like a quantum system that interacts with the local environment),<br> but probably it is not, according to some studies.<br> <br> However, other studies have shown that non-locality seems to be very "robust".<br> <br> <br> <font face="arial" size=2 color="blue"> <h3>5. A few words on "Many Worlds" and "Many Minds" Interpretations: </h3> <font face="arial" size=2 color="black"> QM is absolutely astonishing by itself, but when we go to the Many Worlds interpretation, the excitement-level "shifts gear"...<br> <br> We know what the Copenhagen Interpretation globally means:<br> <br> An a quantum system, initially in a superposition of possibly many states, appears to reduce to a single value<br> of the states, after interaction with an observer (that is: if it's being measured).<br> <br> So, at the moment of measurement, the wave function describing the superposition of states,<br> appears to collapse into just one member of the superposition.<br> <br> In figure 3 above, we already have seen a few simple forms of a superposition of states.<br> <br> Take a look at figure 3, example1, again. Now, suppose, that in a subtle manner, we rephrase the former statements like so:<br> <br> <B>A superposition expresses all possible <U>"alternatives"</U> for finding the value of a certain observable.</B><br> <br> Expressed in <I>this way</I> it get's somewhat more plausible, that <I>all the other</I> "alternatives" may have realized<br> in other "branched off" Universes.<br> <br> Above is not exactly the way that Everett originally formulated it.<br> His theory goes "more or less" like described below. But whatever your opinion will be of the MWI, it really <I>does</I> resolve some paradoxes in QM,<br> like the strange "collapse of the wave function", and even provides a solution for the non-locality puzzle (section 2).<br> And..., some core aspects of the "Decoherence interpretation" (section 4), looks remarkably to the central statement of MWI.<br> <br> In MWI, there is no "collapse of the state vector". Suppose you do a measurement on a quantum system.<br> Before you actually perform the experiment, the system resides in superposition, meaning in all possible states at once.<br> This is what we already new from an undisturbed quantum system.<br> <br> Now you perform the measurement, and you find a certain value. In MWI, different versions of you will have found<br> all the other possible values of the observable. It is as if the current Universe has "branched", or "forked", into<br> multiple Universes where each version of you, is happy with it's own private value.<br> <br> I hear you think.. <I>"Will then the Universe be rebuild N times, at each ocurrence of such an event and so on and so on..?</I><br> No. The trick is in the superposition. The alternatives "are already there", so to speak.<br> <br> Everett realized, that the observer (with measurement device), and the system, forms a deep intertwined system.<br> <B>Each</B> "wave" of the superposition will "sort of interact" with the observer-measurement device.<br> From a mathematical perspective, this pair will split off, and further evolve independently from all the other possible "pairs" of<br> the {wave elements of superposition - observer}.<br> Hence, a number of independtly forked Universes will occur.<br> <br> Do you see the resemblence with the Decoherence theory? Only this time, no environment driven pointerstates are created,<br> but contrary all "relative states" will "start an existence of their own".<br> <br> But, intuitively, you might say, as I do, "this can't be the way the Universe operates..."<br> Indeed, many physicists nowadays say that the MWI theory does not provide an adequate framework on how a<br> many-branched tree of Worlds comes into existence.<br> <br> <br> <font face="arial" size=2 color="blue"> <h3>6. Parallel Universes and the "Wavefunction-less" model of Poirier. </h3> <font face="arial" size=2 color="black"> Around 2012, an interesting model was established by Bill Poirier.<br> <br> He sort of "scrapped" the "wave function" or "state vector" completely, and assumed parallel (thus multiple), classical-like universes,<br> where observables of entities (like particles) have well-defined classical values.<br> His theory treats the collection of universes as an ensemble, and this only creates the "illusion" that<br> a particle might be non-localized in position or momentum (or any other observable).<br> So, while a particle might only appear to have a stochatic character (probability) in some observable, it's actually only<br> due to some "indifference" in which universe the oberver resides.<br> <br> This supposedly explains why QM might "just look" as intrinsical stochastic, but it's actually the interactions between those universa,<br> that sits behind the observed effects.<br> <br> Poiriers mathematical framework, is often called a "trajectory-based" Theory of (Relativistic) "Quantum" Particles.<br> <br> Instead of his original article, I personally find the following 'follow up' article of much more interest, since the authors<br> provide for explanations for (for example) the double split experiment, quantum tunneling and that sort of typical QM manifestations.<br> If you like to see that article, you might use <a href="http://arxiv.org/abs/1402.6144">this link.</a><br> <br> <br> <font face="arial" size=2 color="blue"> <h3>7. A few words on de Broglie - Bohm "Pilot Wave" Interpretation</h3> <font face="arial" size=2 color="black"> This rather peculiar view was first developed by de Broglie in the late twenties of the former century. Then, later on<br> around 1952, it was picked up again by Bohm who made quite some further progress on this theory.<br> <br> Strangely, it became never so popular during the 20th century, compared to the Copenhagen interpretation, and later, decoherence.<br> However, I seem to notice some gaining in interest (by simply scouting articles), since 2000 or so.<br> <br> Note that it was de Broglie who first attained a wave-length to a typical corpusculair entity like an electron.<br> <br> While the Copenhagen interpretation, and it's "collapse", is quite hard to link to reality, the "Pilot Wave" Interpretation<br> re-introduces again some classical features again. Not literally, but essential the theory states that we have a real particle,<br> with an accompanying pilot wave, which can be regarded as a "velocity field" guiding the particle.<br> Bohm further defined an "oncology" or framework on the essential ideas, which made the wave to be compatible with<br> Schrodingers equation, and thus further is deterministic (in the sense of given initial conditions, the further evolution<br> can be calculated).<br> <br> If you are interested in a mathematical framework of this theory, I advise to Google on "Pilot wave arxiv",<br> which should return many scientific articles.<br> <br> Amazingly, since the early 2000s, it was discovered that small oildrops in a bath of oil, show striking<br> similarites with the core idea of the Pilot wave guidance.<br> Maybe you like to see the following YouTube clip:<br> <br> <a href="https://www.youtube.com/watch?v=nmC0ygr08tE">The pilot-wave dynamics of walking droplets</a><br> <br> If you have viewed this clip, then you saw a great pictorial "emulation" of the key concept of this theory.<br> <br> <br> <font face="arial" size=2 color="blue"> <h3>8. A few words about Weak Measurements and the Two State Vector Formalism: </h3> <font face="arial" size=2 color="black"> If there is something else quite stunning in recent findings in QM, it must be the implications of the socalled<br> "Weak Measurements" and the Two State Vector Formalism.<br> <br> Ofcourse, again different <I>interpretations</I> are possible, but one implication seems to be that<br> if you measure an observable without (hardly) disturbing it (and then ofcourse you need to repeat that many times<br> to get any significant result to standout above the noise), then it seems that;<br> <br> Pre-selected results (in the past), <U>and</U> post-selected results (in the future), may have impact<br> on what you measure presently.<br> <br> Take a closer look at those last few words: it's not the normal causality that we are used to.<br> <br> These new formalisms use a time-symmetric model, instead of the usual "standard" approach used in QM.<br> <br> If you want to read more, take a look at:<br> <br> <a href="weak_measurements.htm">a few notes on "weak measurements" and QM paradoxes.</a><br> <br> <br> <br> <br> <br> </body> </html>