The Many Worlds of Quantum Mechanics

Greetings from Sihanoukville, Cambodia, or at least the waters immediately off. I’m here as part of Bright Horizons 19, a two-week cruise on the Holland American ship Vollendam, in collaboration with Scientific American. We started in Hong Kong and have been working our way south, stopping a few times in Vietnam, and after this we’ll briefly visit Thailand before finishing in Singapore. A fascinating, once-in-a-lifetime experience, even if two weeks is an amount of time I can’t honestly afford to be taking off. Been getting a touch of work done here and there, but not as much as I would have liked, in between dashes ashore to sample the local cuisine. Although the local cuisine has been pretty spectacular, I have to admit.

My job here is to give a few talks about physics and cosmology to the folks who signed up for the package — a public audience, but the kind of people whose idea of a good time while sailing the South China Sea is hearing talks about molecular biology or world history. Mostly my talks are variations of themes I’ve spoken on frequently before — the Higgs boson, the arrow of time, dark matter and dark energy. But to spice things up I decided to throw in something new, so I wrote up a talk on The Many Worlds of Quantum Mechanics.

And here it is — the slides, at least. The content is roughly based on my explanation in From Eternity to Here, with a few improvements thrown in.

Two basic goals here. One is to introduce QM to people who don’t know much more about it than a vague notion of “uncertainty” or “fluctuations.” And in particular, to focus on the conceptual foundations, rather than any of the other perfectly legitimate angles one could take: the historical development, the calculational basics, the experimental evidence, the role in modern technology, and so on. Hey, it’s my talk, I might as well concentrate on the parts I’m most fascinated by. So there’s a discussion of entanglement and decoherence that is a bit more specific and detailed than one would often get in a talk of this type, even if it is enlivened by silly pictures of cats and dogs.

The second goal was to give a subtle sales pitch for the Many-Worlds interpretation. Really more damage control than full-on hard sell; the very idea of many worlds is so crazy-sounding and counterintuitive that my job is more to let people know that it’s actually quite a natural implication of the formalism, rather than a bit of ad hoc nonsense tacked on by theorists who have become unmoored from reality. I’m happy to bring up the outstanding issues with the approach, but I do want people to know it should be taken seriously.

Comments welcome, especially since I’ve never tried this approach in a talk before. Of course by only seeing the slides you miss all the witty asides, but the basic substance should come through.

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67 Responses to The Many Worlds of Quantum Mechanics

  1. I had a 5 minute flip and will look again and try to solve your problem later, but a couple of quick comments. The first is a need for mechanisms – I will track the deductive logic of your approach, but whether there are intact alternative interpretations using mechanisms is the issue. That would be the proof, rather than measured events based on probabilities necessarily from limitations to measurement itself and the frames of position and motion, for example, as well as rotation and tension.

    The conclusions based on measurement need to account for the limitations to measurement before expressing confidence. In using position and motion to measure (relative) momentum, uncertainty is an issue of measurement and not a property of mass. All mass continually moves and positions or repositions, but we are limited either to measuring motion or position. You cannot freeze frame a position in space OR time and measure its “frozen” motion in space AND time, you can only closely approximate its motion, and likewise when motion is known but not position.

    Until science can come to grips with how the limitations of measurement itself drive the need to use probabilities (opening the magic door to interpretation of what the probabilities mean). Mechanisms are the key, rather than probabilities. Your deductive analysis may be replaced by a more useful paradigm I write about in my free book at (geometrical design, not spiritual). I will get back to you about the answer to your specific slide show.

  2. I just had a quick flip through From Here to Eternity – its actually much clearer and quicker to scan that long page than trying to work through the “simplified” slides. You do rely fundamentally on the inability to measure motion and position (as momentum) at the same time to open the magic door to interpretation. It is a limitation to frames of measurement and not a property of mass. I will get back to you.

  3. Mitchell Porter says:

    Jack M wrote

    “For the more advanced, David Wallace has recently published a tour de force defense of MWI against all comers.”

    Wallace may be articulate but his ideas are trash. I think I can’t overemphasize how barren they are.

    You say there are many worlds, Mr Wallace – how many of them are there? “… it is a non-question to ask how many.” (From page 16 here.)

    What about the Born rule, Mr Wallace? Why do observed frequencies go with the square of the amplitude? “… rational agents in an Everett universe must act in accordance with the Born-rule probabilities” (from page 3 here).

    Hopefully it is obvious that the first answer is a non-answer. What’s wrong with the second answer requires more explanation.

    There is a formal notion of rationality from game theory: to be rational is to maximize your payoff. In a situation of uncertainty, this means to maximize your expected payoff, so not just the payoff of various possible outcomes must be considered, but also the probability. It is irrational to stake everything on a million-to-1 outcome, even if the payoff would be enormous, because that outcome is probably not going to happen… This “decision-theoretic” notion of rationality therefore depends logically on a prior notion of probability. The fact that the outcome is improbable, is logically prior to the fact that betting on it is irrational.

    However, Wallace, and before him David Deutsch, want to explain the Born probability rule of quantum mechanics, by inverting this logical dependency. They begin with a certain notion of what constitutes rational action in a quantum multiverse, and then derive from this the probabilities that they want.

    I need to point out something else in order to explain what’s going on here. If the basic theory is that there are Many Worlds, and if event A is observed to be twice as common as event B, one might suppose that this is because worlds containing event A are twice as numerous as worlds containing event B.

    But it is actually not so easy to get definite worlds out of a quantum wavefunction in a non-arbitrary way. This is why Wallace wants to say that there is no particular number of worlds: if he can be vague about worlds, that will help his case, he doesn’t have to overcome this problem through the awkward step of adding extra structure to QM.

    However, if there is no definite number of worlds, then the Born probabilities can’t be explained by the relative frequencies of events in the multiverse. That is why he and Deutsch would even consider the sort of contorted argument that they produce.

    But the argument is nonsense, and so is the earlier idea that Everett worlds can be fuzzy things like clouds, without sharp objective distinctions between them.

    The latter idea is nonsense because if the Many Worlds theory is right, you reading these words inhabit a particular Everett world; but if the existence of a world is only a vague approximate thing, a matter of convention, then the same must be true for the existence of anything in that world, including you. The vagueness of worlds would imply that your own existence is something less than absolute fact.

    I regret the abstractness of this argument (some people get it, some don’t), but it is because Many Worlds advocates generally refuse to specify, clearly and exactly, what the worlds are, that one has to dig this deep and show why vagueness about worlds is not an option. If they actually had a theory, it could be discussed in a more rigorous way, and there is nothing to stop them from making a genuine theory of interacting multiple worlds, except for the difficulty of that task.

    But instead they have an “interpretation”, which is to say, a wall of words, a set of constructs which are rhetorical rather than mathematical.

    Anyway, I give up. Reader, please consider yourself warned. These people – many-worlders – do not have a theory, and they cannot back up the claims they make.

  4. DEL says:

    Mitchell: that “These people – many-worlders – do not have a [scientific] theory,” stems from the fact that there exists no experiment or observation that can pit MWI against Copenhagen and thus decide between them, or against both. (See the better parts of the previous post+comments on falsifiability.) But Copenhageners fare no better, and that’s why both fan groups duly call their positions “interpretation” rather than “theory.”

    One cannot do science or think science without a theory, but one can—though with appreciable cognitive difficulty—do without outlandish interpretations. See my Feb. 13 comment to this post and I hope you help tip its rating towards the green.

  5. John Duffield says:

    DEL: your previous comment noted. You know how you said “The wave function does not ‘collapse’ upon observation, as it isn’t a collapsible physical object”. Jeff Lundeen would say its something that’s actually there in the lab. And have you ever looked at the optical Fourier transform? Think of a photon as an extended non-local wavelike entity. Think of an electron in a detector as more of the same. When they interact, imagine something like an optical Fourier transform occurs. Imagine the photon gets converted into a dot at the detector. Which is at one slit. Which the photon then travels through. But if there is no detector, the photon travels through both slits. Like this.

  6. Interesting John, if I read you right, you are reading photons right. Photons would have characteristics when not detected that differ from any Fourier form they take when detected, but I am still wondering about the appearance it actually has when not detected, in your last link. That seems to be a reasonable explanation of the result of an interference pattern, but I think physics still needs to take a step beyond the distinction between ‘as observed’ and ‘when not observed’ to explain the double slit pattern (and redshift between galaxies). That explanation “might” still be merely a probability wave, rather than a diagram of the mechanism itself.

    Lost frequencies from one form of “interference” – by gravitons to photons between galaxies, might have a consistent thread to interference by gravitons to photon passages through slits. A galaxy is big, but its light reaching us here with consistent redshift is still affected by a “graviton” field all the way to receipt. My supposition is that the void is thick with graviton strings and loops, and that they always interfere, in different ways, with photon passages. Even in a quiet lab gravitons extend between apparatus in regular light speed wave patterns.

    Gravity being omnipresent, we only know it relatively as “weight”, but that is quite something considering a human mass held to earth by a void with “gravitons”, which must be immense in a void. And invisible, unlike photons. In a way, we live in a uniform fluid of which we are unaware, and in a lab that fluid as a graviton field is sufficient to affect photons passages by establishing regular wave patterns everywhere according to motion and position of masses – or instruments.

  7. BobC says:

    A very basic style/content comment: I found the inclusion of the masthead for key papers to be especially evocative, visceral, almost tactile, concretely linking the physicist (through their actual work) with me, the reader.

    Combining images of august papers with images if kitty cats and doggies did bend my mind a bit.

  8. John says:

    @ John Duffield

    Do you have more information on what Jeff Lundeen would think? I would agree, and I think it would be the exact opposite of what DEL stated. I don’t think I am going to be able to help applying at the website you gave. Any extra information may come in handy when trying to make up my CV. This is really the kind of opportunity I have been waiting for and been wanting to do for some time. Any extra information would be much appreciated. Thanks.

  9. mike says:

    All in order to not understand aether has mass and is what waves in a double slit experiment.

    “The word ‘ether’ has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. . . . Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. [..] It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with ‘stuff’ that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo.” – Robert B. Laughlin, Nobel Laureate in Physics, endowed chair in physics, Stanford University

    Matter, a piece of window glass and stuff have mass.

    In a double slit experiment it is the stuff which waves.

    “any particle, even isolated, has to be imagined as in continuous “energetic contact” with a hidden medium … If a hidden sub-quantum medium is assumed, knowledge of its nature would seem desirable. It certainly is of quite complex character. It could not serve as a universal reference medium, as this would be contrary to relativity theory.” – Louis de Broglie, Nobel Laureate in Physics

    “According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense.” – Albert Einstein, Nobel Laureate in Physics

    The relativistic ether referred to by Laughlin is the hidden sub-quantum medium referred to by de Broglie is the ether which propagates light referred to by Einstein.

    By relativistic ether Laughlin is saying you can’t know the state of the ether. You can’t know if the ether flows or not. You can’t point to an object and say, “I know that object is at rest with respect to three dimensional space”.

    Same for de Broglie. de Broglie is saying the hidden medium of de Broglie wave mechanics can not “serve as a universal reference medium”.

    Einstein says the ether does not consist of individual particles which can be separately tracked through time. This is Einstein’s way of discussing the relativistic ether. If we can’t know if the aether consists of particles or not then we probably can’t know if the ether flows or not. If you can’t know if the aether flows or not then it isn’t an ultimate reference frame. That’s without even attempting to discuss the notion of flows relative to what? Itself? Our Universe? What if our Universe is moving through three dimensional space? How would we ever detect its motion?

    The ether of relativity is relativistic.

    ‘Einstein: Ether and Relativity’

    “More careful reflection teaches us however, that the special theory of relativity does not compel us to deny ether. We may assume the existence of an ether; only we must give up ascribing a definite state of motion to it, i.e. we must by abstraction take from it the last mechanical characteristic which Lorentz had still left it.”

    Einstein defines motion in terms of the aether as the aether does not consist of individual particles which can be separately tracked through time. The same for ponderable matter.

    Ponderable media is defined as the aether does not consist of parts which can be tracked through time.

    “ponderable media, as consisting of parts which may be tracked through time”

    The mechanical characteristic Einstein takes away from the aether is its immobility.

    “It may be added that the whole change in the conception of the ether which the special theory of relativity brought about, consisted in taking away from the ether its last mechanical quality, namely, its immobility.”

    Meaning, the aether of relativity is mobile. Meaning, the aether of relativity is displaced by the particles of matter which exist in it and move through it.

    The following analogy explains it best.

    “Think of waves on the surface of water. Here we can describe two entirely different things. Either we may observe how the undulatory surface forming the boundary between water and air alters in the course of time; or else-with the help of small floats, for instance – we can observe how the position of the separate particles of water alters in the course of time. If the existence of such floats for tracking the motion of the particles of a fluid were a fundamental impossibility in physics – if, in fact nothing else whatever were observable than the shape of the space occupied by the water as it varies in time, we should have no ground for the assumption that water consists of movable particles. But all the same we could characterise it as a medium.”

    if, in fact nothing else whatever were observable than the shape of the space occupied by the aether as it varies in time, we should have no ground for the assumption that aether consists of movable particles. But all the same we could characterise it as a medium having mass which is displaced by the particles of matter which exist in it and move through it.

    Watch the following video starting at 0:45 to see a visual representation of the state of the aether. What is referred to as a twist in spacetime is the state of displacement of the aether.

    “Imagine the Earth as if it were immersed in honey,” says Francis Everitt of Stanford University in California, the mission’s chief scientist. “As the planet rotates, the honey around it would swirl, and it’s the same with space and time.”

    The ‘swirl’ is more correctly described as the state of displacement of the aether.

    You have a mesh bag full of marbles that you spin in a supersolid. If you can’t know if the supersolid consists of particles or not you should still be able to determine the state of displacement of the supersolid as determined by its connections with the marbles and the state of the supersolid in neighboring places.

    The state of the aether as determined by its connections with the Earth and the state of the aether in neighboring places is the state of displacement of the aether.

  10. John Duffield says:

    Marcus: IMHO in its own little way, a photon is a graviton. To try to visualize this, imagine a stiff lattice. Put your hands in back-to-back and top to bottom, and pull. The lattice now has a lemon-like “pulse” of distortion in it. And it’s a stiff lattice, there is no outer edge to this distortion. This is a snapshot of a photon. Wherever the distortion is the photon is, so the photon takes many-paths. The slope of a horizontal lattice line denotes E, and as the photon moves say left to right at c the rate of change of slope denotes B. In the middle of the pulse four-potential is at a maximum but E and B are zero, as per Aharonov-Bohm. A lattice square that is skewed is a spin1 virtual photon. A lattice square that is vertically shortened is a spin2 virtual graviton. But skewed squares are shortened.

    John: nothing much, see Jeff Lundeen’s website and my comment of 13th Feb above where I quoted from his semi-technical explanation. Also see Aephraim Steinberg’s website and the physicsworld article In praise of weakness.

  11. Erik Bray says:

    Very interesting; I may have to borrow these slides and see if I can use them myself to explain QM to my relatives 🙂

    One typo, I think, on slide 25 that I’m surprised no one mentioned yet: It reads something like “if we observe Ms. Kitty under the table, we know Mr. Dog is in the yard with 100% certainty”. Shouldn’t it be Mr. Dog is in the doghouse, or have I just not had enough coffee yet to properly function? 🙂

  12. mike says:

    When a downconverted photon pair are created, in order for there to be conservation of momentum, they are created with opposite angular momentum.

    As they are propagating with opposite polarization, they can determine their partner’s location and momentum based upon their own.

    They are not physically or superlumanally connected.

    They are entangled as they can determine each other’s state.

  13. DEL says:

    Phillip Helbig: It was Schrodinger, indeed. See his 1926 Annalen der Physik paper:

  14. “Phillip Helbig: It was Schrodinger, indeed. See his 1926 Annalen der Physik paper:”

    I guess that proves that I am smarter than the Time Lord. Where do I collect my reward? 🙂

  15. David Kagan says:

    John Duffield, there is a danger in the approach you are suggesting. Consider a system of entangled photons:

    |up>|down> – |down>|up>

    what wavefunction would you ascribe to the first photon? What about the second? Or are you suggesting that in such a situation, there aren’t individual photons at all, but only a composite system?

  16. John, that might take me a while to solve. Its an interesting idea though, equating the two. I would definitely say the same “material” and both rotating, but photons would detach to move regularly between particles (I will avoid your alternative use of photons for now) and gravitons must stay attached in some way to be able to move with particles as a source of field variation. I use a void as background for simplicity, and Newton reinterpreted merely to allow more properties to masses than he imagined in a void. Action- reaction, and space-time as background to motion and position remain from Newton. Einstein is preserved only from his SR reconciliation, which apply in a void using the properties of masses uncovered in the 20thC. I reject the pure Isotropy of GR and its necessity that we live on the surface of a hologram, and allow all mass to exist in a void and expand under gravitational energy conversion from rest in a compressed state with that given potential – linearly in direct opposition to its own gravitational field.

    With that background, undoubtedly debateable on all points,, photons become backwards rotating loops, right or left, that have direct interference by gravitons extending in a void and making a “fluid” through which all mass moves. In my model, the relationship is more fundamental even than photon-photon, or photon-particle, or graviton-graviton, or graviton-particle. They are glued together by shearing each other in common passages at light speed between particle sources that carry both fields in their travels. So, yes to photons and gravitons being the most fundamentally tied masses in existence, and yes to materiality (photons might actually be gravitons concentrated on themselves to literally bounce rather than always attract by loops), but they would each preserve their forces at all times in their separate phenomena, and so no ultimately to them being the same thing, as such. But I will try to have a look at your outline above.

  17. That reads right, Mike.

  18. DEL says:

    John Duffield:

    1) For some reason, the Jeff Lundeen link and associated URL do not work for me.

    2) If, as I understand, Lundeen claims he measures psi, does he measure both its real and imaginary parts? He must, because, as far as I know, the wave function of QM is the only physics quantity that is inherently complex, its complexity not just a matter of mathematical convenience or convention. In contrast, in classical waves, exp(ikx) usually means either cos(kx) or sin(kx). And no classical wave equation contains i explicitely, as Schrodinger’s does. (Boy! does that look like a mathematical miracle-maker contraption!)

    3) Now, what about the matrices of Heisenberg’s matrix mechanics? Matrix mechanics is known to be mathematically equivalent to Schrodinger’s wave mechanics. So what is it that Lundeen measures, a psi wave or some matrix? If these are concrete physical objects, they can’t be both right.

    4) As a Caltech Ph.D. (Aeronautics, 1985,) with a long career of signal processing behind me, of course I know about the Fourier transform, optical or otherwise. And my basic QM education did include the trick of turning a localized particle into a spread wave, and vice versa, courtesy Mr. Fourier.

    4) The key word in your reply is “imagine.” No, I would not imagine a photon performing the Fourier trick on interacting with an electron—I cannot imagine either of them having reached the necessary college level. If it’s any consolation, I also do not believe that a macroscopic dumb projectile calculates its way along its trajectory according to Newton’s laws.

    5) My point, and my philosophy of science, is this: scientific theory is strewn with “entities” and “narratives” that help us process it in our imagination, apply it in calculations, design experiments and interpret their results. But the success of a theory doesn’t necessarily mean that these entities and narratives are real physical objects and processes. And the best proof for this view is the history of science: those entities and narratives do have a way of being replaced once in a while. So how can one of them actually literally collapse? (It might collapse, figuratively, when a paradigm shift comes and discards it.)

  19. John Duffield says:

    David: I’m afraid I side with Einstein, and consider “spooky action at a distance” entangled photons to be a misinterpretation. See re Bell.

    Marcus: IMHO it’s important to distinguish virtual particles from real particles. See this. Virtual photons relate to the evanescent wave aka near field. Hydrogen atoms don’t twinkle, there aren’t any actual photons zipping back and forth in an electromagnetic field. Likewise for gravitons in a gravitational field. IMHO the key to it is here where Einstein referred to a field as a state of space. Think about the state of space around an electron.

  20. mike says:

    Marcus, I take it you are referring to my understanding of entanglement, correct?

    Understanding entanglement is one downconverted photon’s ability to know the state of the other means there are no such things as hidden variables.

  21. Joe Dickinson says:

    This from a biologist way out of his depth. I have never been able to understand how we know that “there is no reality (e.g., regarding the position of an electron) until we make an observation, causing the wave function to collapse”. How do we exclude this interpretation: the electron has a real position all along and the “wave function” simply describes our ignorance? Similarly for entanglement. Two particles interact and separate. When we observe one, do we really instantaneously influence the other, or do we simply learn something about it that we previously did not know? How can you make that distinction other than on grounds of some ideology? I think of a quadratic equation: two solutions are equally good. Now we add another relevant equation that “chooses” between those two. Should we say that the second equation mysteriously influenced the first, or just that new information let us choose? Help!!

  22. vmarko says:

    @ Joe Dickinson:

    “This from a biologist way out of his depth. I have never been able to understand how we know that “there is no reality (e.g., regarding the position of an electron) until we make an observation, causing the wave function to collapse”.”

    Try these keywords for Wikipedia and Google: “counterfactual definiteness”, “local realism”, “Bell’s theorem”, “reality”, “locality”, “measurement”. A good places to start reading:'s_theorem

    HTH, 🙂

  23. Yes Mike, that seems more sensible than saying there is a spooky connection.

    John, that’s good advice, I should look more at how physics interprets a “field”. I tend to think of virtual photons as unobserved, particularly inside atoms. Photons of light or heat are lost and gained when atoms compound or interact and a field is evident.

    Maybe I should broaden my thinking, but the idea of a field concerns me – a wave is fine as one interpretation, or a particle, or collapsed wave, and so on, but its purpose is to exchange fixed momentum, whether observed or not, and I would propose a three dimensional object rather than a “space” filled by (?). A photon can be an object with wave-particle properties depending on the flexibility of its rotations, particularly if it has a flexible back end.

    In my book I use a flexible back end to a three dimensional rotating object, as a photon, to enable it to couple and decouple with a particle to allow for the particle motion by its flexible rotating back end. I use a two step process of front end at light speed and back end adjusting to redistribute the photon “position” across a particle surface rather than more directly by a front end always at light speed. This enables photons to be a c in a void and as measured by moving particle – in a void. No need for abstruse interpretations of SR without a void. Assumed rest for exchanges is by a field mechanism.

    So we may have different ideas about fields and what they do. As a space filler, sure they decouple and recouple and in between they use a void for their wave-particle passage – as a rotating loop that drags its tail. I will read more about your interpretation of particle and field behaviour and coupling, as I know from other reading that current physics does not explain things the way I do, and yet we purport to explain the are the same events.

  24. Joe Dickinson, I agree with you. Much of science is badly explained.

    How on earth a simple limit to measurement – being unable to freeze frame a motion (space AND time) while freeze framing its true position (in space OR time) – became misunderstood as a property of mass is beyond me.

    We have an absolute frame limit to measurement. This is not magic – it arises by definition. Position is space OR time. You measure where it is or when it is in relation to where it was or when it was. You can fix a true position. But motion is by definition space AND time, and it is not a fixed position. It moves by definition and cannot be frozen to be known exactly when a position is known – by the same measurement at the same time.

    How can you measure literally different things at the same time? You can only measure a smear of motion at a fixed position – at best. Or a smear of position if motion is known. You are not allowed, but definition, to fix a position while measuring motion. The position is a smear.

    They have an inverse relation. I use that relation in my photon model (above) to enable a positional adjustment to take some of the momentum and maintain a fixed motion when photons couple and decouple with particles.

    How on earth this all became interpreted as mass itself being in a state of uncertainty rather than measurement, is beyond me. But the fact is that it has been quite logically extended on that basis into deductive “follow-on” in Sean’s slide show and so on. They are just saying “if” mass is uncertain, this is what is “might” mean as a deductive follow-on of logic. “If”.

    I go my own way as far as science is concerned because I have found so many blunders, if the above counts as such. I know several that are firmly rooted in current science. Anyway you can read more about my grumbling in my free book (click my name for my site) – all good natured and always logical, as above. You may not agree with me., but you should understand me as I abhor abstraction.