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Cosmology, Quantum Mechanics & Consciousness Message Board › The mechanism within quantum mechanics. What actually happens?

The mechanism within quantum mechanics. What actually happens? Collapse or no collapse?

lan B.
user 10895495
London, GB
Post #: 250

I'll kick off with this then. Andrew may well have -- in fact probably already has -- come across this Wiki entry, but the majority of the rest of you (??) probably haven't. (From the Wiki entry Schrödinger's cat.):


Copenhagen interpretation

Main article: Copenhagen interpretation

The most commonly held interpretation of quantum mechanics is the Copenhagen interpretation.[5] In the Copenhagen interpretation, a system stops being a superposition of states and becomes either one or the other when an observation takes place. This experiment makes apparent the fact that the nature of measurement, or observation, is not well-defined in this interpretation. The experiment can be interpreted to mean that while the box is closed, the system simultaneously exists in a superposition of the states "decayed nucleus/dead cat" and "undecayed nucleus/living cat," and that only when the box is opened and an observation performed does the wave function collapse into one of the two states.

However, one of the main scientists associated with the Copenhagen interpretation, Niels Bohr, never had in mind the observer-induced collapse of the wave function, so that Schrödinger's Cat did not pose any riddle to him. The cat would be either dead or alive long before the box is opened by a conscious observer.[6] Analysis of an actual experiment found that measurement alone (for example by a Geiger counter) is sufficient to collapse a quantum wave function before there is any conscious observation of the measurement.[7] The view that the "observation" is taken when a particle from the nucleus hits the detector can be developed into objective collapse theories. In contrast, the many worlds approach denies that collapse ever occurs.


Many-worlds interpretation and consistent histories

Main article: Many-worlds interpretation

In 1957, Hugh Everett formulated the many-worlds interpretation of quantum mechanics, which does not single out observation as a special process. In the many-worlds interpretation, both alive and dead states of the cat persist after the box is opened, but are decoherent from each other. In other words, when the box is opened, the observer and the already-dead cat split into an observer looking at a box with a dead cat, and an observer looking at a box with a live cat. But since the dead and alive states are decoherent, there is no effective communication or interaction between them.

When opening the box, the observer becomes entangled with the cat, so "observer states" corresponding to the cat's being alive and dead are formed; each observer state is entangled or linked with the cat so that the "observation of the cat's state" and the "cat's state" correspond with each other. Quantum decoherence ensures that the different outcomes have no interaction with each other. The same mechanism of quantum decoherence is also important for the interpretation in terms of consistent histories. Only the "dead cat" or "alive cat" can be a part of a consistent history in this interpretation.

Roger Penrose criticises this:

"I wish to make it clear that, as it stands, this is far from a resolution of the cat paradox. For there is nothing in the formalism of quantum mechanics that demands that a state of consciousness cannot involve the simultaneous perception of a live and a dead cat",[8]

However, the mainstream view (without necessarily endorsing many-worlds) is that decoherence is the mechanism that forbids such simultaneous perception.[9][10]

A variant of the Schrödinger's Cat experiment, known as the quantum suicide machine, has been proposed by cosmologist Max Tegmark. It examines the Schrödinger's Cat experiment from the point of view of the cat, and argues that by using this approach, one may be able to distinguish between the Copenhagen interpretation and many-worlds.


Objective collapse theories

According to objective collapse theories, superpositions are destroyed spontaneously (irrespective of external observation) when some objective physical threshold (of time, mass, temperature, irreversibility, etc.) is reached. Thus, the cat would be expected to have settled into a definite state long before the box is opened. This could loosely be phrased as "the cat observes itself," or "the environment observes the cat."

Objective collapse theories require a modification of standard quantum mechanics to allow superpositions to be destroyed by the process of time evolution.

That's all for now, apart from registering for the purposes of possible further discussion by others my own disagreement with Sir Roger's conclusion. Roland Omnès himself -- in The Interpretation of Quantum Mechanics approvingly quotes Enrico Fermi's down-to-Earth emphasis of the apparent paradox (in view of QM's officially absent commentary on the vanishing of quantum superpositions "at the point of measurement" -- however one takes that to mean!):

"Why isn't the Moon fuzzy when we look at it?" His answer: because it is being illuminated continuously by other objects! This is a form of interaction, which could form the basis of some form of measurement procedure. I would respond to Sir Roger by pointing out that quantum states per se are unobservable. It is only classical-like mixtures of "comminuted" quantum states that we can observe, and even then it is only the mixture -- and not the individual compositional quantum states themselves that we are in principle able to observe. For instance, the quantum-phase component of superfluid helium II cannot be observed. As soon as some atom has interacted with the outside world then it drops out of superposition,and all that the experimenters are able to see are classical-liquid remnants which have appeared at the positions where they have been recorded during the observation by non-classical means!

The point to remember from the "quantum realist" point of view -- held not only by myself but in an objective collapse sense by Sir Roger also -- is that at whatever level of description of physical reality, the ultimate components are always quantum states. They never disappear!

Ian



A former member
Post #: 156
Ah yes, what is really going on in the universe at the smallest scales? What actually are electrons and photons and how exactly do they do what they appear to do? In other words how are we to interpret the mathematical formulae of quantum theory? In other words what is the 'correct' interpretation of quantum theory in terms of what is really going on? The answer to these questions is that we don't know and possibly may never be able to find out. Because the quantum realm is at or beyond the limits of any further scientific investigation by way of exploring ever smaller scales. 

So, looking up 'quantum interpretations' in Wikipedia, we find 14 categories of alternative interpretation, some of them quite wild. There are probably some more. Decoherence is not explicitly mentioned in the list as one of the main categories but it  is an important part of the whole quantum story. We can all have different opinions about such unknowns and for my part I have always scorned the many- worlds interpretation, in which  schrodinger's cat is both dead and alive at the same time on the grounds that it exists in different 'branches of reality'. I feel that the 'many worlds' interpretation relies too heavily on the formulae from which it emerges. No, a cat is either alive or dead and is not both at the same time. Decoherence explains that perfectly well and is the most natural and sensible explanation of the cat whose fate is determined by a single quantum particle - on whether or not such a particle is is emitted from a radioactive atom. 

But as I understand it decoherence does not explain everything when we examine the minutiae of quantum behaviour.

-  Is the emission or otherwise of a photon from an atom (within any particular period of time) explained by decoherence? If so precisely how? 
- How is the standard mathematical formalism explained by decoherence?
-  Every photon which is emitted is also absorbed. How does decoherence explain the 'choice' of which atom to be the recipient of a fast-approaching photon wave?  

So it seems to me, and as I have previously noted the Stanford Encyclopaedia agrees with this view, that decoherence explains the interface between quantum and classical behaviours but does not explain fundamental quantum behaviours in terms of the standard formulation of the theory.
lan B.
user 10895495
London, GB
Post #: 251

Thanks for maintaining the interest, Andrew!

My take on the decoherence situation is that quantum states seem to be intrinsically "gregarious". (Maybe "promiscuous" would be even more fitting!) Therefore, should any quantum state comprising some fimite set of "elementary particles" or stable associations thereof such as atoms or "small molecules" propagate through space with each of these elementary components obeying the de Broglie relation λ = h/mv ..

[ .. Allthough conforming to the Uncertainty Principle such that their individual locations cannot be specified with sufficient precision to be able to identify their positions on any length scale comparable to their own classically/chemically/crystallographica­lly derived lengths and diameters unless they're travelling very quickly (in which case we would ascribe "classical" adjectives to them in any case). This fact alone would suggest to me that the notion of particle -- as opposed to that of discrete component -- is a mistake. Anyway, back to the plot now ..]

.. Then "the chances are" -- especially in situations where the "particles" described by the relevant wavefunction are moving at velocities comparable to those of some eventual interactor/target such as an array of CCDs in a Young's Interferometer, and if the speed component of these velocities is sufficiently small that the "particles" are able to remain in each other's vicinity for long enough that there is, again, "a significant chance" of redistribution of energy such as the complete loss of some component photon's "identity" and the corresponding rise in energy of some, say, electron within the target -- the chances are that some interaction will take place, due to the fact that in penetrating the extremely complicated association of mutually decoherent quantum states which "pseudo-classically" comprises some bulk physical object the density of quantum states rises very fiercely in comparison to that of the preceding "empty space" traversed by the photon. Large-scale correlations therefore very quickly break down in favour of the formation of progressively more local ones. It can be seen that such an empirically confirmed process is the direct analogue of the "comminution" of macroscopically collimated mechanical energy within moving parts, friction-generating surfaces, and heat engines which causes the mutual disordering of formerly collimated velocity-components and the corresponding increase in the entropy of the system, its immediate surroundings, or both. This is a change in quantum state: at least one discrete component ("the photon") of some radially, spatially propagating quantum state has "transferred its allegiance" to some quantum subset belonging to the impenetrable solid ahead of it. An even more homely image would be that of the square dance, in which one could regard the fundamental process as the continual switching of partners in a continual "evolution of square dance state" but the number of human dancers remains conserved. Of course, here the analogy strictly speaking breaks down because quite often the number of elementary particles within such interactions is not necessarily conserved. (For instance, in situations of non-perfect light reflection, some absorption always occurs; i.e. some photons cease to exist entirely, totally yielding their enery either to excited electron states or otherwise via so-called phonon or roton interactions by coupling to the internal degrees of freedom -- or "heat" -- of the system.)

Now I freely confess to using the phrase "the chances are" twice during the foregoing expression of my current opinion on the matter. Is the situation then entirely stochastic? Or are there instead determining constraints -- not necessarily timelike in operation and, therefore, strictly speaking non-causal in nature? Decoherence theorists are as ready to bite the bullet of indeterminism as any other interpretative school of quantum mechanical thinking. Omnès does so, for instance. However -- as I have droned on at perhaps tedious length several times already elsewhere -- non-locality opens up the possibility of a form of determination which is near-orthogonal to the time-axes of each of the interacting players. Again,as indicated previously and elsewhere,I am following the lead of quantum theoretician Sandu Popescu in entertaining this intriguing idea.

Could it be that the process of interaction (and, therefore, of concomitant change-in-overall-quantum-state) is itself recursive, depending on nth-order internal interactions, perhaps tending towards some asymptotic limit? I'm not nearly competent enough to attempt any mathematical modelling by way of establishing the consistency of such an interlinked set of ideas with the rest of what physics holds beyond reasonable doubt to be true.

It is clear, however, that at least within bulk matter the very process of photon absorption is itself non-local. Symmetry considerations suggest that this may be true of emission also. (In 1956 the Twiss/Hanbury-Brown experiment showed, for instance, that photons are emitted in pairs, and show "anti-bunching", negative correlation!) This tentatively answers your question as to "choice of recipient atom". It may be that global consistency considerations -- as in the consistent histories interpretation, the flip side of decoherence -- drastically narrow the subset of permissible (either) "interaction sites" or, even more abstractly, the eventual "loci of representation of global interaction".

[ .. Continued .. ]








lan B.
user 10895495
London, GB
Post #: 252

[.. Continued.. ]

>How is the standard mathematical formalism explained by decoherence?

It isn't! On the contrary, recognition of the logical permissibility of the effect arose as a result simply of consideration of the further consequences of interaction between the already-accepted postulates of QM. One could say that this kind of process is a hallmark of the coming to maturity of some subject. The "mere" establishment of some empirically corroborated and consistent set of postulates such as within SR, GR or QM no more furnishes a complete understanding of the relevant subject-matter any more than does consideration of the rules of chess and the pieces' starting positions on the board provide any insight as to how best to beat an experienced opponent! It wasn't until the 1960s and Murray Gell-Mann that quantum theorists began to "think into the game" in any seriously in-depth manner other than that of the development of statistical methods such as by Bohm and, later, Bell in order to test the 1935 EPR conjecture.

Again, ironically -- as Penrose honestly admits -- it is the collapse theorists who have fundamentalpostulatory bugbears to sort out, because the acceptance of "collapse" necessary entails a modification of the postulatory foundations of QM!

Having said all this, I confess to a partial hybridisation with Sir Roger's own position: even if there is non-local determination of change of quantum state, there would still seem to be some fundamentally missing desideratum if we are to avoid total stochasticity. Along with him, I agree that some sort of energy-minimisation or energy-equilibrating process may be at work. The questions then arise: What is its scope? Exactly how non-local does the determination need to be? Aren't there, also, entirely nuclear effects such as radioactive decay which seem about as screened-as-could-be from environmental interaction? (Although even here there remain outstanding questions of nuclear structure still to be resolved, and at such high energy densities it might be impossible to rule out interaction with vacuum polarisation effects, for example.) Sticking my neck out still further, I could conjecture that the Uncertainty Principle in itself implies a kind of intrinsic fuzziness to the notion of position, such that there is "a limit to the degree of resolution -- by analogy with the use of lenses and microscopes in order to expand finer detail -- of what constitutes a "history" in the first place. If one were to transect such a "fuzzy point", would it be clear that despite its pseudo-singularityit is in fact homogeneous in regard to properties pertaining to every coordinate location of its cross-section? .. And in such a sense (i.e. in terms of potential scope for such "orthogonal, time-free interaction", might it be possible to take advantage of the crucial property of "many worlds" without actually be (distastefuuly!) obliged to have any?

I hope that I've managed to communicate the final point effectively, if somewhat tersely. If not, please seek further clarification. I think most of us will agree that I've gone on far too long already!

Ian

A former member
Post #: 157
Thank you Ian, for conceding that decoherence does not explain the standard mathematical formalism of quantum theory and does not answer my other questions either. That means that you must now agree with me and with Stanford Enc that decoherence is not an interpretation of quantum theory, as I have been saying all along including the earlier discussion that we had on this topic. It means that I am correct to say that decoherence explains the interface between quantum and classical phenomena and does not explain what is really going on at the foundations of the quantum world. 

Your verbose and woolly reply does possibly hint at some last-ditch attempt to slide out of agreeing that I am right, but let me set aside your hopeless appeals to the game of chess, square dancing etc etc and let me point you again to the Wiki definition of 'quantum interpretations'. There you will find yourself totally boxed into a corner with no escape. An interpretation has to specify the physical meaning of the mathematical entities of the theory. You agree that decoherence does not assign any physical meaning to the projection operator. QED.

Of course it might be possible to find the 'truth' in a modified version of the standard theory, maybe including your ill-formed idea of some kind of space-like causality. But steady on, let's not re-write the best and most accurate scientific theory ever invented just to help you win a lost argument! Let's wait for the science to tell us if the theory needs to be re-written and let's see where the science takes us. Otherwise you are heading down a woo-woo direction and Jazz will be claiming that his idea of 'synchronicity' is as valid as yours - if not a direct consequence!

By the way if you do want to expound on space-like causality then please do it properly, preferably with some attaching maths so we can see what precisely you are on about. My first question to you then will be: in what way does this idea differ from the time-symmetric interpretations (including Cramer's transactional interpretation)?

Thank you!
lan B.
user 10895495
London, GB
Post #: 253

Thank you Ian, for conceding that decoherence does not explain the standard mathematical formalism of quantum theory

.. indeed not; Omnès goes as far as to claim that "quantum theory dictates its own interpretation" (if decoherence is, as said, taken as a serious consequence of the universally accepted QM postulates) ..

and does not answer my other questions either.

.. Well Omnès is the first to admit that it doesn't explain the singling out of the history of our collective experience -- or "which world?" -- but then like everyone else (except the various schools of local hidden-variables theorists) including the Copenhagenists he is prepared to leave the selection process to sheer probability.

That means that you must now agree with me and with Stanford Enc that decoherence is not an interpretation of quantum theory, as I have been saying all along including the earlier discussion that we had on this topic. It means that I am correct to say that decoherence explains the interface between quantum and classical phenomena and does not explain what is really going on at the foundations of the quantum world.

The problem with QM has always been -- in the absence of any interpretation, which thus far have been extraneous to the theory itself -- precisely that it lacks any explanatory interface with the world of classical physics (of which the world of our everyday experience is a subset)!

Any eventual successful interpretation needs to address this "interface problem", for that is the problem!


Your verbose and woolly reply does possibly hint at some last-ditch attempt to slide out of agreeing that I am right, but let me set aside your hopeless appeals to the game of chess, square dancing etc etc and let me point you again to the Wiki definition of 'quantum interpretations'. There you will find yourself totally boxed into a corner with no escape. An interpretation has to specify the physical meaning of the mathematical entities of the theory. You agree that decoherence does not assign any physical meaning to the projection operator. QED.

The projection operator singles out the actual, measurable, pseudo-classical state of some decohered quantum system! (I know that you accept decoherence as an empirical true effect.)

Of course it might be possible to find the 'truth' in a modified version of the standard theory, maybe including your ill-formed idea of some kind of space-like causality.

In that case I'm afraid that you still belong to the "Old Guard" within physics, who steadfastly refuse (in dwindling numbers!) to this day to accept the results of the Aspect, et al, experiments.

(Kuhn was right then: one has to wait for the previous-generational paradigm-bearers to die before the newer viewpoint is able to find general professional acceptance.)

But steady on, let's not re-write the best and most accurate scientific theory ever invented just to help you win a lost argument! Let's wait for the science to tell us if the theory needs to be re-written and let's see where the science takes us.

Yes, true: the world of physics was obliged to wait untilthe '90s and the advent of experimentalist teams led by people such as Anton Zeilinger and the huge tranche of decoherence-investigation research programmes which have been spawned therefrom.

Otherwise you are heading down a woo-woo direction and Jazz will be claiming that his idea of 'synchronicity' is as valid as yours - if not a direct consequence!

By the way if you do want to expound on space-like causality then please do it properly, preferably with some attaching maths so we can see what precisely you are on about. My first question to you then will be: in what way does this idea differ from the time-symmetric interpretations (including Cramer's transactional interpretation)?

Sorry: the whole point about the Bohr-EPR dispute ever since it explicitly emerged in 1935 is precisely that orthodox, uninterpreted QM allows for non-locality..

..it was the local realists such as Einstein and Schrödinger who didn't like Bohr's "anti-realist" advocacy and insisted on the incompleteness of QM precisely because pristine QM, served neat, does permit non-locality. (After all, who in the proverbial month of Sundays would ever take such a "magical" notion seriously if it weren'tfor the exceptionless, untrammelled empirical success of QM?)


A former member
Post #: 158
Ian
Out of the 7 comments that you've pasted into my last message the first three and the last two have no useful relevant content.

The 4th comment refers to an undefined phrase: the 'pseudo-classical state'. I do not recognise that as a term of standard quantum theory. It seems more like a woolly idea of a quantum state that is very close (whatever that might mean) to a classical state. In which case it is a superposed quantum state and is not the output of a projection operator but is instead the result of the time evolution of former quantum states via the Schrodinger equation or similar.

The 5th comment attempts to characterise me in uncharitable terms. You don't seem to have learnt not to classify people, especially when you get it wrong. Save the classifying for your stamp collection. Remember, I have pointed out several times before over the past year or so precisely where you got it wrong (on several occasions, each time in some different way) and here you go again. As far as I am aware the non-locality aspect is largely an 80 year-old consensus, reinforced and confirmed by the more modern work to which you refer.

Remember, you are the one who has hinted at "the possibility of a form of determination which is near-orthogonal to the time-axes of each of the interacting players". Understand that I am not criticising non-locality, I am referring to your "form of determination which is near-orthogonal", whatever that is. Or is it just a convoluted way of saying that the wave function and entangled states are inherently non-local, ie of saying nothing new whatsoever? It sounds like you are suggesting a new idea, some weird idea of causality operating in a space-like direction, in which case you need to explain and defend exactly what it is that you have been hinting at instead of behaving like some school bully, attempting and then failing to denigrate others.

Trisha
user 10455453
Lehigh Acres, FL
Post #: 12
Interesting question that is at the heart of some of the problems in interpretation. I'm afraid I can't follow all of what has been said. I still don't fully understand decoherence (among other things). Neither the Copenhagen interpretation or the many worlds view pleases me. I have what may seem a strange question though. I am not as well read as you chaps on the subject, but what is the deal with superposition? I suppose I am getting at the Schrodinger cat thought experiment or the "is the moon there if you aren't looking at it" issue. My understanding of the two slit experiment is that it is a probability distribution of where the particles are. If that is so..it is a measuring tool and not an actual reality. The particles do not have to literal exist in all possible states at the same time, its just that we cannot as yet measure exactly where they are when traveling and instead just observe the interference pattern which indicates a wave. To me this indicates ...we do not know...not that the particles exist in all states. So I am thinking perhaps the ensemble interpretation works for me regarding the resolution of Schrodingers cat. Otherwise it seems to me there is a confusion of the tools of measurement with what is being measured. I suppose in this view there is no collapse, because there is no superposition in the first place.

But I can't help but feel I am missing something though. Perhaps if I keep reading my confusion will abate a bit...but I don't understand why so many assume superposition is literally real in the first place. I know the quantum zeno effect has been observed to be real, so that is one possible reason..but again..couldn't it be that our tools at present make the act of measuring interfere so that the "observation" isn't merely looking but disturbs the natural state?
A former member
Post #: 161
At least, Tricia, your favoured 'Ensemble Interpretation' has the distinction of being first on the list of 14 given by Wikipedia in the section on 'quantum interpretations'. Apparently lots of expert practitioners of QM still adhere to either the Copenhagen interpretation or to 'Many worlds'. I suspect they mostly don't care and don't think much about the foundational questions.

The table in the Wiki article http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics­ shows 'wave collapse' as just one of the issues. We could equally discuss whether the wave function represents something real or not, which links with your point about what superposition really means. Other abstract criteria are also shown in the table headings. The different interpretations cannot be separated by present scientific means, but you can prune them down by specifying your preferences about wave collapse etc. I do have my own ideas about this but I'm not motivated to talk about it unless someone really wants to know, which I rather doubt. It seems almost but not quite like discussing which is the best football team.

lan B.
user 10895495
London, GB
Post #: 254

Interesting question that is at the heart of some of the problems in interpretation. I'm afraid I can't follow all of what has been said. I still don't fully understand decoherence (among other things). Neither the Copenhagen interpretation or the many worlds view pleases me.

Snap! ( .. And as I've pointed out in previous postings these days relatively few practicing experimental physicists are still prepared to accept Copenhagen other than as in furnishing a series of doctrinal, pedagogical technique-stuffings (as in pâté-de-foie-gras!)

For an excellent overview of the current status of decoherence, its implications for solving the Measurement Problem, and, best of all, what it (putatively!) means, why not link to Evans and Thorndike's online-readable monograph Quantum Mechanics at the Crossroads. Unfortunately since it's a pdf I haven't got the right software to OCR, cut and paste it, but here's the link (in bits, in order to disguise the fact that it's an address from the moronic Meetup automatic address-censor):

http://...

faculty.washington.edu

/afine/decohere

nce.p

df



I have what may seem a strange question though. I am not as well read as you chaps on the subject, but what is the deal with superposition? I suppose I am getting at the Schrodinger cat thought experiment or the "is the moon there if you aren't looking at it" issue.

Philosophers of science -- along with philosophers in general -- distinguish between so-called epistemic issues on the one hand -- concerning our own state of relative ignorance of how things stand with respect some question -- and ontological issues on the other --concerning how things stand with nature, independently of human knowledge, intervention, or indeed the existence of humanity at all. Interpreted this way, the Schrödinger's Cat conundrum was seen by Bohr at least as epistemic. As an anti-realist (or instrumentalist) about quantum mechanics -- (Bohr): “There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature”, Bohr was not committed to believing in the latent coexistence of multiple physical states pertaining to one and the same entity. (I.e. was not committed to interpreting superposition as "actual".)

My understanding of the two slit experiment is that it is a probability distribution of where the particles are.

Yes, but only after the fact. The probabilities are always calculated according to some formalism or other -- usually using the Schrödinger Equation itself, although this is not essential, and sometimes a Heisenberg/Pauli-type matrix approach is used instead. Sometimes "naked operators" are used as in outlining quantum computation problems, or predicting the Bell outcomes in, say, polarised photon correlation measurements. The formalism in question isn't particularly important, depending more on the familiarity of the would-be calculator with the technique in question rather than with anything physically substantive. (Which is why IMHO questions as to "the agreement of the physical world with what the formalism says" are, to say the least, missing the point. In QM we are not faced with a perfectly comprehensible – albeit, admittedly, highly counterintuitive – situation in which the results of calculation nevertheless stick accurately with our classical physical insight all the way. The fact is that we simply and entirely lack overwhelming professional consensus as to how to frame what is physically happening).

If the entity/entities traversing both slits at once are classical waves, then there is no reason why a speckled, particulate pattern should appear on the photographic plate at the far end of the apparatus. If they are classical particles, then the situation is even worse, because then the (observed!) interference effects are ruled out. The distribution of detected “photon impacts” should be bimodal, centred on the 2 slits, but it isn’t!

The crucial point is that no classical picture of the slit-traversing is compatible with what is observed. The wavefunction formalism (say) says nothing about the individual outcomes, and doesn’t in itself even give the probabilities directly, but only their so-called amplitudes (which must be squared in order to obtain the probabilities themselves). All this is obtained by direct analogical extrapolation of the classical, 17th century algebraic modelling of ripple propagation and interference upon the surfaces of ponds and the like.

Yet this wavelike aspect to the mathematical modelling is important. The Heisenberg Uncertainty Principle dictates that only the product of 2 so-called conjugate measurables can be found, leading to the result that any attempts to obtain arbitrarily exact measurement of the position of some entity will only open up greater imprecision in regard to establishing its (simultaneous) momentum (and conversely). This variation is not unique. We get the same trade-off should we decide to measure, instead, the energy of some system undergoing some change-of-state versus the time taken in order to accomplish the transformation. The crucial point here is that the dimensions of the algebra which precisely defines the lowest physically achievable bound to the uncertainty are always [M][L]^2. [T]^-2. (“Spin” has exactly the same dimensional expression!) If this consequence is not epistemic but ontological—and because it appears within the dimensional expression it couldn’t be anything but ontological – then strict causality drops out of physics! Given that that is the case, the alternative probabilistic description leaves us puzzled as to precisely what “change of state” now actually means within “fundamental” physics!

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