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I think I can explain what Little wants to say here. There is, as you suggest, supposed to be something like an interference pattern *at the source*, produced by the interference of all those reverse waves coming from the screen. I can see why you are puzzled about this, because it's not clear where that interference pattern is *exactly* or how it's supposed to help. It would seem to have to be located practically at a point, namely, the source. But I think Little has a sensible answer here. Basically, it is that, yes, the interference pattern is right there at the source, crammed into a point. But thinking that's some kind of problem for the theory is based on losing sight of how the theory is supposed to work. Remember the idea is that each point on the screen is supposed to be sending out waves in all directions, and that the waves from a given point on the screen are somehow "tagged" so that they are coherent with other bits of wave sent out by that same point on the screen, but *in*coherent with (and so unable to interfere with) waves from *other* points on the screen. So let's just think about some one point on the screen, and if we can get straight on that we'll have the whole thing, because each point on the screen acts similarly (but independently). So there's some point on the screen sending out these waves, some parts of which make it through the slits and arrive at the source. Depending on the relative path length between the parts that went through the two slits, the parts might be in phase or out of phase (or something intermediate) at the source. The idea is that this wave interference occurs, and it is the overall/net amplitude of the wave -- right there at the source -- which determines the probability that the wave will "tickle" the source just the right way and thereby trigger a photon particle to be released. If there is constructive interference, the wave amplitude will be large, the tickling will be intense, and so lots of photon particles will be released by the source "into" that wave. On the other hand, if there is destructive interference, the wave amplitude will be zero, there will be no tickling, and hence no photon emission. And if the interference results in an in-between amplitude, a proportionately in-between number of photons will be emitted. And of course the idea is supposed to be that once the source emits a photon particle "into" a given wave, the particle just follows the wave back to its source, i.e., to the particular spot on the detection screen that emitted that wave. And so you can see how different points on the screen will end up receiving different numbers of particles, and so how the observed interference pattern develops. I think there are some questions about this that ought to be answered in a really serious theory (as opposed to a half-baked idea). For example, what determines which of the two possible paths a given particle follows back through the apparatus? What is the nature of the "tagging" that is required to prevent the waves from different points on the screen from interfering with each other, and how is this "tagging" preserved when the waves scatter into new directions at the slits? And there are lots more questions like that one could ask. My attitude is that, if there weren't these other clearly (to me) fatal problems with the theory (pertaining to the EPR-Bell type experiments) I might be interested in thinking more carefully of what other such questions should be asked, and demanding answers to them. But since I already know with certainty that the theory is wrong, and worse, that the whole idea of and motivation for constructing a relativistically local theory is unviable and corrupt, there's no point wasting time worrying about such details. Thomas, you said you have a background in physics and have looked into Bohm's theory, but that you don't think Bohm (or anybody) has the correct interpretation. What specifically are your objections to Bohm's theory? You also said something I didn't understand at all: "Throwing out the waves as they do in the Copenhagen interpretation I think ignores the evidence, but I don't know that anyone has gathered the evidence and has presented a good overall theory at this time." In what sense do they "throw out the waves" in Copenhagen. The Copenhagen interpretation of course uses a wave function.

OK, here are some thoughts on Little's rather strange addendum to his book. To begin with, it was interesting to me that the name of the file that contained this document was "Bohmian non-explanation of Insbruck." (Too bad he misspelled "Innsbruck" here and in the document -- probably an unintended "fix" by the automatic spell-checker.) This (and also the title supplied inside the document itself) suggest that, in his mind, the main purpose of this document is to attack the claim that the explicitly-nonlocal Bohmian theory can explain the data from this experiment. Leaving aside (for now) the fact that all of Little's criticism are completely stupid, it is very curious that Little feels the need to attack Bohm's theory on this point. First, it's not like he hasn't already made it abundantly clear in the book that he rejects Bohm's theory and equates superluminal causation with "magic." And second, why bother? Since 1905, all physicists have regarded superluminal causation as anathema -- as something to be avoided practically at all costs. So, if Little really thought his own theory could account for the data in these experiments in a local way, why would he waste his time "piling on" against non-locality? Why not, instead, just explain (in explicit mathematical detail) how the local explanation works? That he still doesn't do the latter is therefore telling. On this same point, it is perhaps worth highlighting Little's statement that "TEW might not be the correct explanation of the Insbruck experiment." Little claims, both in the book and here in this "addendum", that the TEW *can* account for the results of these experiments. (Of course, he conspicuously fails to back that claim up with any demonstrative calculation, and it's certain from Bell's theorem that no such calculation could possibly exist, but nevertheless the *claim* is there.) I think everybody understands that a theory which makes the correct prediction for a given experiment could nevertheless be wrong. For example, orthodox QM makes the correct predictions for the Innsbruck experiment, but everybody involved here, at least, agrees that orthodox QM is not true. So if all he means here ( in this confession that "TEW might not be the correct explanation") is that, despite being able to make the right predictions for this and other experiments, it might in principle turn out that TEW is wrong, why bother saying so? It goes without saying. So there must be something else on his mind. What could that be? Perhaps -- and this is admittedly just speculation -- this is his way of appeasing that little voice of honesty in the back of his head -- the part that knows that (even after many years of trying) he is unable to lay out a demonstrative calculation, and instead has to just emptily (and dishonestly) assert that TEW does make the right predictions. That is, maybe -- I would actually say, probably -- what Little actually means when he writes that "TEW might not be the correct explanation of the Insbruck experiment" is this: "Maybe it will turn out that the results of these experiments can never be understood from within the TEW framework." If that speculation is correct, then that little part in the back of Little's head is right. The results will never be able to be understood from within the TEW framework, because one of the pillars of that framework is the insistence on relativistic local causation, and that is *precisely* what Bell's theorem tells us *must* be given up in order to understand this experimental data. Which brings us to Little's comments about Bell's theorem in this addendum. I said in my original "book review" that Little obviously doesn't understand (and/or is evasive about) Bell's theorem. That same ignorance/evasion is on further display in the addendum. What his discussion here comes down to is the claim that, in TEW, the physics that determines the eventual outcomes of the two measurements occurs at the source, as opposed to being somehow "carried" by the individual particles as they fly away from the source. (It is interesting that, in the course of this discussion, he appears to be retracting something he said on page 71 of his book -- though the exact identity or scope of the retraction is unclear.) Anyway, why does Little care about this distinction? Because he believes the following: But this is in fact not what Bell's theorem shows at all. Indeed, far from proving that the state of one photon (just prior to its measurement) must depend on the state of the other photon (at that same instant), the theorem actually *allows* for this kind of non-locality -- and *still* manages to establish that such theories are in conflict with experiment. That is, even the sort of non-locality Little is alluding to here (namely, the individual particles just prior to measurement fail to have their own individual well-defined states, but the state of each one somehow depends on the state of the other, distant one) is *insufficient* to account for what is observed in the experiments. Theories, in short, have to be *really* non-local in order to make the right predictions. That's what Bell's theorem proves. (If you want to understand that in detail, go back and look at the derivation of Bell's theorem I presented in the book review, and notice in particular that the symbol "L" refers to the joint state of the photon pair. Giving each photon its own distinct state is of course an allowed special case of this, and is therefore "covered" by the theorem. But the theorem actually only assumes something weaker, i.e., it allows that maybe you can only -- as in orthodox QM -- give some kind of nonlocal joint state assignment for the pair as a whole.) If you can follow that, it should then be obvious why Little's rhetoric is so ridiculous. If *even* the sort of theory he describes (by mentioning QM, namely, the sort of theory in which there is some strange sort of nonlocal dependence of the state of one photon on that of the other) is *insufficiently nonlocal* to account for the experimental results, then obviously his own theory (which is supposed to be *fully* local) isn't going to be able to account for them either. Let me put this another way. Let's make up some terminology for two different sorts of nonlocality -- call them "kinematical nonlocality" (by which I mean the sort of nonlocality in which spatially separated objects sometimes fail to have their own distinct/separate states, but instead must be described by some sort of nonlocal joint state for the multi-object and spatially-extended "whole") and "dynamical nonlocality" (by which I mean some kind of causal influence that propagates from near the measurement interactions on one side, to the measurement interactions on the far side). Bell's theorem proves that, in order to be empirically viable, a theory *must include dynamical nonlocality* -- and this is true whether or not it includes kinematical nonlocality. Now along comes Little. He says (wrongly) that Bell assumes as a premise that there is kinematical nonlocality. Then he confuses that (falsely alleged) premise with the conclusion of Bell's argument, and infers that what Bell's theorem *proves* is that you have to have kinematical nonlocality. Then he claims that TEW contains no kinematical nonlocality and so is immune to Bell's theorem. It's quite ridiculous. I admit that, for someone without any background in physics, Bell's theorem (and this whole constellation of issues) is tricky and confusing. But it's really not rocket science. It's just a matter of getting clear on the assumptions, understanding how they are motivated by and related to relativity's prohibition on (dynamical!) nonlocality, following a bit of relatively trivial algebra, and then understanding how to relate the theoretical derivation to experimental results. This is all standard stuff for physicists. I cannot believe that Lewis Little (who does, after all, have a PhD in physics) is unable to follow this. But if he is, i.e., if he's really just thoroughly confused about Bell's argument, then, as I said in the essay, he has no business writing on this subject, let alone claiming to have discovered a new gaping loophole in Bell's arguments. And if, as I strongly suspect, he *isn't* that stupid, all of this meandering word salad, designed to obfuscate and distort the truth, is quite vicious. But let me drop that and just summarize the physics. Consider the version of Bell's theorem I laid out in my essay. Here we assume that there are functions like A(a,L) which describe how a given polarization measurement will come out (H or V, or +1 or -1, or whatever terminology you want to use) depending on the orientation of the polarizer and the physical state of the object being measured (which, remember, is not even just the one impinging photon, but the whole *pair* -- and even including, if you want and think it's relevant, other physical facts which are, say, stored back at the particle source). Just to flesh this out a little, what is being *excluded* here is that the outcome of Alice's measurement (that is: A) should depend on how Bob (remember, at the last possible second!) freely chooses to orient *his* polarizer (that is: b). We also exclude the possibility that A should depend on the *outcome* of Bob's measurement, B, though that is not even really an additional assumption since we are here (for convenience, because it is another axiom of TEW) assuming determinism. So... does Little want to *deny* that such functions as A(a,L) exist for his theory? This would seem to require rejecting one of the following: (a) determinism, ( local causality (which manifests itself here precisely in the assumption that Alice's outcome A cannot depend on Bob's last-minute freely-chosen *setting*, b), or © the idea that Alice's outcome depends on facts pertaining to her measuring apparatus (which are covered by a) and facts pertaining to the photon pair and source (which are covered by L). If he wants to deny (a), then we'll just switch to one of the other versions of Bell's theorem that doesn't assume determinism. Given his repeated insistence that a violation of local causality is tantamount to "magic", he can't want to deny (. So maybe he wants to deny © -- but then, whatever else he wants to say the outcomes depend on, we can just include that in "L" and return to the original argument. (Unless, that is, he wants to say the outcomes depend on something that is so situated spatio-temporally that its inclusion would violate local causality, in which case we're back to denying (.) There's really just no "out" here. Which I guess is why he resorts to rhetorical obfuscation. But I'm happy to leave the matter open as a challenge. Somebody who agrees with Little or thinks they understand what he's trying to say here (and so presumably thinks I'm misrepresenting or misinterpreting him) -- please come here and explain it to me. Don't tell me why Bell's theorem doesn't apply. We can worry about that later. Just *demonstrate* that TEW can make the correct predictions for this experiment. And, under the conditions I mentioned earlier (e.g., you can't smuggle in nonlocal causation!), I'll write you a check for a thousand dollars and stand corrected. Let me now change topics slightly and say something about Little's comments about Bohm's theory and "active information" in particular. The phrase "active information" is something Bohm himself introduced several decades after his original 1952 papers, as a way of talking or thinking about the way that particles are, according to his theory, guided by the associated "pilot wave." The basis for this was the (rather technical) fact that the "force" which the associated wave-field exerts on a particle is independent of the *strength* of the field, but depends only on the *structure* of the field. Bohm analogized this to a ship at sea on auto-pilot, receiving "instructions" on how to move from signals encoded in the surrounding electromagnetic field, which signals had been broadcast (say) by some distant naval station. The idea was that, if the signal is weak (say because there is some fog between the station and the ship), but still strong enough that the ship's equipment can "pick up the station", the ship will still move exactly the same way. That is, the "instructions" are independent of the overall *strength* of the signal, but dependent on the *structure* of the field (i.e., what we humans would describe as the information encoded in it). As opposed to what? Well as opposed to something like the Earth sitting in the gravitational field of the Sun -- the force on the Earth just being proportional to (i.e., exclusively dependent on) the *strength* of the field at its location. My point in explaining what Bohm meant is just to underscore that this terminology -- "active information" -- was merely a sort of analogy to highlight one interesting aspect of his theory. So it's extremely misleading and unfair for Little to latch onto this terminology as if it was somehow essential to or even constitutive of the theory, and criticize it. And it's even more misleading and unfair to then launch off on a rationalistic tirade about how "information" is a term which cannot be used literally and properly to describe purely physics interactions, and so (Little concludes) Bohm's theory is all bound up with subjectivism and anti-realism and "magic". It's just completely dishonest rhetoric. And anyway, the whole "active information" terminology/analogy isn't even something that any of Bohm's proponents use or endorse. It came from a period in Bohm's life that even the staunchest supporters of Bohmian Mechanics recognize as one where Bohm-the-person was a little kooky and into all kinds of crazy mystical nonsense. To get a little technical, ever since Bell raised people's awareness of and appreciation for Bohm's theory back in the 60s and 70s, people have generally conceived of Bohm's theory in "first-order" terms (meaning that the basic dynamical law for particles is an expression for their *velocities*) rather than the "second-order" terms (meaning that the basic dynamical law for particles is an expression for their *accelerations*) in which Bohm himself formulated the theory. The two are mathematically equivalent, so it really is the same theory either way, but how you think about it is a little different depending on which formulation you endorse as fundamental. And the point is, Bohm's idea of "active information" was tied to his "second-order" formulation of the theory, so this really just isn't any part of what people today who support and endorse Bohmian Mechanics mean or use. So in every possible way, Little's criticisms of Bohm's theory are misguided, straw man obfuscations that only serve to display his ignorance and dishonesty. Finally, what is there to say about Little's further polemics trying to equate superluminal causation with "magic"? Nothing that I haven't already said in the original essay. Superluminal causation is only "magic" if you arbitrarily include relativity theory as part of what you define as the acceptable, non-magical alternative to "magic." But relativity is hardly in the same category as "A is A" or whatever basic metaphysics ought to be taken absolutely for granted here. Relativity is a theory in physics. Its turning out to be wrong wouldn't violate any principle of metaphysics. And there is powerful evidence to suggest that it might in fact be wrong -- namely, the Innsbruck (and other related) experiment(s) as interpreted via Bell's theorem. And if that's right, i.e., if relativity does turn out to be wrong, it *obviously* and *in no way* proves that there's no reality, or that the world is governed by magic, or anything else like that that we're supposed to be able to rule out a priori on purely philosophic grounds. Phew. Any questions?

Harry Binswanger forwarded me a document that Lewis Little sent him. I gather that it's some kind of "addendum" to Little's just-published book, and is relevant to the issues I've raised on this thread. I have no direct contact with Little, but Dr. Binswanger and I interpreted Little as wanting this document to be as widely circulated as possible, so I am going to post it here -- and then comment on it in a subsequent post. (In the event that HB's and my interpretation was wrong, and this document was not intended for public distribution, someone should please inform me of that and I or a moderator will take it down. But I'm pretty sure that's not the case, or else I wouldn't post this here in the first place.)

Ifat: that's a fair question. I think I disagree with some of the premises behind what you write, though, so let me try to clarify a few things. First, I am not asking people to take my judgment on faith. Doing that would have required far fewer words and far less time! I indeed make some strong claims about the shoddy quality of TEW and this book and its author, but I included a ton of details in the essay to back up everything I said. And, for anyone who doesn't agree that I've justified all my claims, I have expressed my willingness to hang around here for a while and provide further details/explanation. In short, I'm willing and able to lay out whatever evidence reasonable people require to grasp the truth of my assertions for themselves. Now, at some level, you are right that some (but not all) of the issues involved here are technical ones, and having an appropriately grounded opinion on such issues may indeed require more background in physics than a lot of people here have or will have or will be able to acquire just for the sake of forming a grounded judgment of TEW. That is: there is indeed an aspect of "expert testimony" to this. As you said, I've made my opinion known, and am at some level allowing and expecting reasonable people (who aren't in a position to judge the physics issues firsthand) to nevertheless be able to form some kind of judgment about me as an expert, in order to make a grounded decision about whether my "expert testimony" can be trusted or not. That's another reason why I want to hang out here for a bit and give people a chance to ask questions, etc. What I'm saying here is that, even for people with (say) zero background in physics who (therefore) aren't in a position to form a first-hand judgment on (say) whether or not Bell's theorem magically fails to apply to TEW, can nevertheless form a first-hand judgment about *me* as an alleged authority on these matters. And I would certainly encourage such people to be trying simultaneously to form a parallel judgment about Lewis Little and his followers. The point is, even for these people who are in the position of having to rely on expert opinion one way or the other (and btw there's nothing whatsoever wrong with that), I am not asking to be acquiesced with *on faith*. I'm just not. So that aspect of your question is really not valid. But there's an even more basic point here. If somebody doesn't have the physics background to form an appropriately grounded judgment of TEW (or Bohm's theory or Bell's theorem or whatever), then why should they have any opinion one way or the other? And in particular, why should they *endorse* and then *publicly proselytize* for something they do not understand and are not in a position to rationally judge? I submit that doing that is irrational and wrong. So think again about what I'm asking for in the final paragraphs of my essay. I'm not actually asking for agreement (blind or otherwise) with my views. I'm just asking that people, recognizing that there are at least some purported "experts" who think TEW is an embarrassment to Objectivism, stop proselytizing for TEW (something they, ex hypothesi here, are not in a position to judge firsthand) under an Objectivist banner. If I'm right, then their doing so is embarrassing and destructive to our shared attempts to get Objectivism the kind of respect it deserves. And if I'm wrong... well, in order to really think I'm wrong, someone would have to learn some more physics so they could judge these things for themselves, or at least interact with me enough (here or elsewhere) to be able to conclude that *I'm* the dishonest crackpot, evidently hell-bent on destroying the most important achievement in physics in the last 200 years. All I can say is that I welcome anyone's honest attempt to arrive at their own rational firsthand judgments, whether of the physics or of me (or of Lewis Little). And my point is that this is *exactly* what people *ought* to do *before* they endorse or publicly proselytize for TEW (or anything else). In short: if someone doesn't want to take the time to make a rational decision between two conflicting pieces of alleged expert testimony, they should at least have the sense to keep their mouths shut about the disputed issues when in public qua Objectivist. I'm maybe rambling a bit (no coffee yet this morning!) so let me answer this part of your question directly: I don't want anyone to (blindly) "take my side" -- if that means, say, endorsing and publicly proselytizing for Bohm's theory. I really don't want that at all. What I want is for people in the position you describe (and who don't want to invest the time to form a grounded judgment either of the physics or of the alleged/competing "experts") to (a) recognize their own state of ignorance on this issue, ( quit endorsing and publicly proselytizing for something they are ignorant of, and © recognize that *maybe* (given their state of ignorance) continuing with that sort of behavior damages and embarrasses Objectivism. Does that clarify? Do you really think that's too much to ask of people, or somehow an unreasonable request? You also asked: It would be wonderful if the book's author would come here and debate the scientific issues. (Actually, it was partly because I thought just maybe something like that would happen here, that I chose to post this here as opposed to, say, posting exclusively to HBL.) That would give almost everyone the kind of data they need to form a rational judgment either of the physics issues, or the personalities. Indeed, such open dialogues between the two sides used to exist, and some of them can still be seen online (see the old yahoogroup "TEWLIP"). I certainly encourage anyone interested to explore those archives -- and also to consider the implications of the fact that, subsequent to its becoming clear that the original version of TEW was a failure vis a vis the EPR-Bell experiments, the TEW supporters have systematically excluded anyone critical of the theory from such discussions and have increasingly hidden themselves away in dark private corners. That's true. Maybe it would help to provide more of my credentials? OK. I graduated from Harvey Mudd College (Claremont, CA) in 1997 with a double-major in physics and philosophy. I was mainly a physicist, but did the philosophy double major because Darryl Wright is the philosophy dept. at HMC, and I wanted to take every course from him that I could. As a junior I took ARI's undergraduate course on OPAR (taught then by Gary Hull) and, in my senior year, started taking courses from Dr. Binswanger at the (then) "OGC", which I continued doing through graduate school and beyond. I won a prestigious NSF graduate research fellowship. I got my PhD in physics from the University of Washington (Seattle) in 2002. My research was in theoretical nuclear astrophysics (mostly neutron star interiors), but even then I was really mostly interested in the foundations of physics. I was the first-ever grad student in the department to be permitted to single-handedly teach a real, on-the-books course for undergraduate physics majors. It was a "senior seminar" on the foundations and interpretation of QM. After grad school I took a job teaching physics at a small private college in New England. While there I have published a number of articles on the EPR argument and Bell's theorem in various places including the American Journal of Physics and Foundations of Physics. I am currently on sabbatical and writing a book version of the freshman physics course I designed and have taught for the last few years -- it covers some standard (and some non-standard) physics material while tracing the historical origins, development, and application of two great pre-20th-century theories in physics: Newton's theory of gravitation and the atomic theory of matter. I am happily married and have two cute and brilliant young sons. Does that help? (I hope it's clear that I'm being a little tongue-in-cheek here, hence the slight sarcasm at the end. I really don't see how any of that could possibly help at all, and I don't think anybody should decide whom to believe, if anyone, in this dispute because of anything that could be conveyed in a bio paragraph like that. But, I suppose, maybe it does help to know that I'm not just some high school kid on a rant -- in case that wasn't obvious already.) Anyway, I actually agree with you that what's needed (for people to form a rational, grounded judgment of *me* qua possible authority) is to interact with me over time. Which is precisely why I've offered to stick around here and answer just this sort of question. So thank you for giving me the opportunity to provide you, and whoever else is reading, some further data.

It's called a "thesis statement". Do you think the body of the essay fails to support my assertions? Or is it that any (admittedly pointed) criticism of Little or TEW is, no matter how justified, going to be dismissed as ad hominem?

I don't understand this at all. It seems like you're just positing that there are certain relations between the various parameters that the wave function depends on. Certainly you can't *derive* from the given function of x1 and x2, say, that "'if you translate space by an amount in one direction" both x1 and x2 "will change by the same amount." I frankly don't even know how to parse what that's supposed to mean. Why should x1 and x2 "change" *at all*? They aren't quantities that take on some one particular value; they are the variables that the wave function is a function *of*. (Maybe you meant that the wave function would remain invariant if a certain N of the 3N variables were increased by some constant amount?) And even leaving that objection aside, your whole answer here begs the question. What do you mean by "Spatial translation"? If all you've got is a field living in some 3N dimensional space, you're not yet entitled to discuss "spatial translation" (referring implicitly to 3-space). You must first either *posit* 3-space as a new axiom for your theory, or show that it somehow emerges from or is already secretly embedded in your field on 3N-space. Sometimes people try to take this last route and argue that you can "read off" 3-space from the structure of the Hamiltonian (in particular the potential energy part, which typically has terms that depend on the 3-spatial separation between particles). But I've never found that at all convincing.

Suppose the universe has one spatial dimension and there are only two particles in it. So you have a wave function that is a function of three variables -- x1, x2, and t. If you tell me that this wave function provides a complete description of physical reality, I can understand that by visualizing a field that spreads over two spatial dimensions and evolves in time. On the other hand, I do not know how I can understand that function of x1, x2, and t as describing two things that move and interact in a 1-D space. So if you are proposing that this function *is* a description of two things that move and interact in 1-D space, it's you who will have to explain it to me. I hope it's obvious how this is the same as what's at issue here. I've just made the numbers smaller to make things simpler. The real version is like this: suppose there are N particles in the real 3-D universe. Then the wave function (ignoring spin and treating things as in NRQM purely for convenience) is a function of 3N "spatial" coordinates (and t). So, if you tell me that function provides your complete description of physical reality, I can only infer that you think physical reality has 3N spatial dimensions and there's some kind of field that lives in that space. I don't know how to get from that picture/ontology to anything remotely resembling the world I see when I open my eyes. So you'll have to explain how that works. Note that this illuminates another important feature of Bohm's theory. There's no problem of "finding" the familiar world of perception in the ontology posited by the theory, because the theory posits particles that move and interact in 3D space -- so, for example, it's going to include cat-shaped constellations of particles, tree-shaped constellations of particles, a me-shaped constellation of particles, etc. Of course the motion of these particles is somehow choreographed by this mysterious object, the wave function, which lives... I'm not quite sure where. But you can at least postpone that puzzle (if it is one) for another day and not have to worry that your theory doesn't include cats and trees and me. Which I think we'd all agree would be a pretty serious worry for anyone who cares about empirical adequacy of theories.

Just one quick comment. There's a dangerous large-scale sort of circularity in the idea that the real external physical world is radically different than how it "appears" to us in consciousness. (Indeed, there are fatal philosophical mistakes built into even that way of talking about the relationship of consciousness to reality, but I want to leave those aside for now and just make a mostly-physics point.) What is the evidentiary chain that leads to MWI in the first place? Well, surely it goes through believing in Schroedinger's equation, which in turn was posited based on how certain famous experiments from the 1910s and 1920s came out. But if MWI is true, then none of those experiments actually had the outcomes we (or, rather, they, back then) erroneously took them to have, and so the whole epistemic motivation for the theory crumbles away. It's, in this sense, not exactly self-refuting, but self-undercutting in a pretty ominous way. It's may also relevant to point out that people who think about these kinds of issues seriously concede that there are some pretty difficult problems like this for MWI -- but, they argue, it's still worth it to take the theory seriously because it's supposed to be the only possible way of saving fundamental relativity (in the face of Bell's theorem, etc.). So it is pretty important that MWI really cleanly allow relativity. But this also turns into a huge problem, since the theory doesn't even posit any kind of ordinary 3+1 dimensional world populated by physical objects. If all there is is the wave function, then the universe is (again contrary to our subjective conscious experiences) a space of some extraordinarily high dimension (roughly, the configuration space for all the particles in it, since that's the dimensionality of the space the wf lives in). But relativity was never supposed to be about anything like that. It's supposed to be about the structure of 3+1 spacetime and how certain relational properties transform between different reference frame in that spacetime. So it's pretty bizarre for MWI to claim to be *the* uniquely relativistic version of quantum theory, when, according to it, there isn't even such a thing as 3+1 spacetime, nor any physical matter in it.

But look at what you're actually saying. The whole physical universe, including your body and brain, is in some massively complicated superposition of states, each of which (taken individually) corresponds to some one familiar/definite way the universe could be experienced. But, in fact, according to the theory, the world isn't that way at all. So how come we experience it to be in one of those familiar/definite configurations? How come we don't experience it as it actually is, namely, in a massively complicated entangled superposition? Because some kind of magic -- which I hold is tantamount to the collapse postulate -- is "put in by hand" (i.e., just arbitrarily asserted as a new postulate) at the physical-universe / mind boundary. Which by the way makes a hash of virtually every foundational principle in Objectivist epistemology and metaphysics (e.g., perceptual realism -- according to MWI every conscious experience anybody has ever had has been massively delusional, in the sense that its "report" about the state of the external physical world is totally false... We see a cat that's definitely dead or definitely alive, but *really* it's neither, etc.). If you want to honestly compare the parsimony of orthodox QM and Bohmian Mechanics, it's a mistake to just say "Bohm adds particles to the ontology, so it's needlessly cumbersome." Yes, Bohm posits both particles and a guiding wave (just the ordinary wave function, for the record). But because of what it "adds" to orthodox QM, it gets to subtract a bunch of stuff -- namely, all of the vague and inconsistent measurement axioms. That is, there is no "measurement problem" for Bohm's theory the way there is for orthodox QM, because, for Bohm, all physical processes are on the same footing -- there's no need to divide the world into subject and object, quantum and classical, speakable and unspeakable, measurements and non-measurements, etc. You have just one set of basic dynamical postulates which apply *all the time*, whether anybody is making a "measurement" or not. Now I gather you won't be too impressed by that comparison because you don't want to advocate orthodox QM, you want to advocate MWI -- which is precisely orthodox QM but with all the measurement postulates subtracted out. And I grant that, if you got a coherent theory that way, it would indeed show that Bohmian Mechanics is not maximally parsimonious (which wouldn't be the end of the discussion, but it'd be something). But in fact you don't get a coherent theory that way. You get something that is, frankly, crazy and unscientific. And, anyway, you end up having to sneak the measurement axioms back in at the mind-matter interface -- which, as Bell once pointed out, is a very uncomfortable place to be doing physics. You seem like a smart guy, and I can only assume you have some interest in Objectivism. So I really don't want this to become confrontational. But you seem to have accepted a lot of dubious ideas from your physics training. The antidote to that is reading Bell. Get a copy of "Speakable and Unspeakable" and start reading it. As I mentioned before, "Bertlmann's Socks" is a great place to start.

Looks like the kind of trash I get in my mailbox at work every couple of weeks. And, no, I don't want to discuss it any further than that. (Because, you know, I'm part of the big conspiracy.)

Someone contacted me privately with a good, critical question about my essay. It amounted to: how come, in the section where I am discussing Little's claim that Bell's theorem doesn't apply to TEW, I interpret him as saying that Bell's theorem is premised on *indeterminism*? The questioner validly pointed out that Little seems maybe instead to be saying that Bell's theorem is premised on some notion of *continuity*. For what it's worth, I stand by my original interpretation of Little's meaning. After all, what Little claims is that it's certain *probability distributions* which are assumed, by Bell, to be continuous. I interpret Little as saying, in effect: 'In QM, there aren't definite discrete predicted outcomes, but only *probabilities* for the possible outcomes, with some (continuous) probability function describing how they depend on the angles involved. Whereas, in TEW, the outcomes are determined, one way or the other (but perhaps depend discontinuously on the angles involved for a given hidden state L). So the theorem doesn't apply.' As I tried to indicate in the essay, it is completely wrong to claim that Bell's argument is premised on indeterminism -- and so there is simply no such issue as whether the allegedly-assumed probability distributions characterizing the allegedly-assumed indeterminism are "continuous" or not. Nevertheless, what I wrote does involve some perhaps-dubious interpretation of what Little wrote. The relevant paragraphs of my essay would indeed have been unfair or misleading if (a) Little meant that the theorem was based on "continuity" rather than indeterminism and ( it is true that some such "continuity" is a premise of the theorem. So let's contemplate that. Unfortunately for Little, though, nothing I said would change even if he did mean to assert that Bell's theorem is premised on "continuity" rather than indeterminism. For the version of Bell's theorem I lay out in the essay embraces not only deterministic theories, but theories that are "discontinuous" in precisely the sense that Little could arguably have meant. The functions such as A(a,L) are in no way assumed to be continuous functions of their arguments. There simply is no such assumption. (It is relevant here that the mathematical derivation of the theorem uses only algebra, not calculus -- there's not even any step in the math where the issue of continuity could possibly come up.) So *whatever* Little might have meant on these pages, he is surely wrong (a) that there is any such limiting assumption among Bell's premises, and ( that the theorem doesn't apply to TEW. In fact, as I have argued extensively elsewhere (and as Bell himself stressed repeatedly), there is only one premise needed to derive a Bell inequality: local causality.

I started a new thread since this was off-topic in the TEW thread. Bohm's original theory was a replacement for standard NRQM, yes. But since then people have found ways to do for (allegedly) relativistic quantum theories (e.g., multi-particle Dirac theory, QFT) what Bohm did for NRQM. Some of the extensions are controversial and/or ongoing research programs, but still. I can tell you're not really up on the literature on quantum foundations or Bell in particular. People seriously interested in these issues use "signal" as a term of art referring specifically to the human activity of signalling (transmitting "information"), which is not coextensive with causal influences. Sending a superluminal signal requires some underlying causal influences that propagate superluminally, but the latter is not a sufficient condition for the former. The relevant causation must, for example, be sufficiently "controllable" that humans can harness it for their desired purposes. This distinction is important, because all the theorems proving that "relativistic" quantum theories are consistent with relativity actually only prove that those theories don't support superluminal signaling -- *not* that the theories don't contain superluminal causation and not that they don't require extra-relativistic spacetime structure. In response to my claim that (even) orthodox QM requires such extra spacetime structure, you asked: The collapse postulate. When a measurement occurs anywhere, the wave function describing (previously-entangled) degrees of freedom anywhere else in the universe changes *instantaneously*. And of course "instantaneously" is not a relativistically invariant concept. It is made to look that way by the fact that all you are ever asked to calculate in QFT courses is matrix elements (so you can calculate scattering cross sections and whatnot). But if you actually step back and think about the story the theory is telling for the evolution of the physical world over time, and what happens when somebody somewhere makes a measurement, and how other things have to evolve subsequently, you'll realize that there's no relevant difference between QFT and NRQM. They both require a collapse postulate to get the right answers, and formulating that precisely requires some un-relativistic concept of a dynamically privileged space-like hypersurface. Wavefunction collapse doesn't "emerge" in MWI. Unless you put it back in by hand at the world-mind interface (i.e., unless you cheat). In response to my claim that Bell's theorem is not actually premised on "hidden variables" (popular belief to the contrary notwithstanding), you wrote: That's not much of an argument, so in response I'll just say: "Yes, it is." And: maybe you should go read some of Bell's own papers. I'd recommend starting with "Bertlmann's socks and the nature of reality" (conveniently reprinted in the book "Speakable and Unspeakable"). It is a brilliant paper. Nothing in the secondary Bell literature (and certainly not whatever textbook you got your information from) comes anywhere close. Pay special attention to footnote 10, where Bell states clearly that his "own first paper on this subject [his 1964 paper that first presented what is now known as Bell's theorem] starts with a summary of the EPR argument from locality to determinstic hidden variables. But the commentators have almost universally reported that it begins with deterministic hidden variables." In regard to Bohmian Mechanics you wrote: Actually we do have evidence that there are particles (think: spots on detector screens or tracks in bubble chambers), and evidence that the motion of the particles is somehow guided by a wave (think: all the little spots make an interference pattern as they accumulate). And by the way, according to Bohm's theory, when you measure the position of a particle, what you "see" is the actual pre-measurement position of the particle. So people who think that these particle positions are somehow "hidden" or "metaphysical" or "unempirical" are just wrong. If anything, it's the wave function that has that status. But I don't see anybody complaining about the wave function in other theories. I don't know what you mean by the word "classical" in the middle sentence. Yes, particles in Bohm's theory follow trajectories. But they are certainly not the trajectories predicted by classical physics. As to the last sentence, it would be nice. But it's of course fallacious to say that, in a situation that two different theories make the same predictions, one of them should be considered "verified" when its predictions are borne out, while the other should be dismissed a priori simply for making the same (empirically verified) predictions. It would be just as valid to say that orthodox QM should be dismissed until or unless it makes some prediction that is different from the predictions of Bohm's theory. The point is, when two theories make the same predictions, and those predictions are correct, you can't cite experiment directly as favoring either one. You'll have to appeal to some other standards, e.g., clarity, seriousness, parsimony, etc. And if you do that, Bohm is going to win over orthodox QM hands down. I strongly disagree with your whole approach here. It's fine to describe physical reality "from an observer's point of view" -- if you mean, for example, using some particular reference frame for defining coordinates and whatnot. But this is very different from giving up the whole attempt to describe physical reality and instead just tossing around symbols, one term from which eventually is supposed to correspond to some kind of subjective conscious experience for some particular subject. I think you misunderstand what relativity is all about. You seem to be confusing it with solipsism.

I understand that that's what a lot of physics texts (and papers in the "Bell literature") say. But I (and many other experts on this stuff) don't think it's correct. First off, as Bell pointed out so eloquently, it is extremely dubious to interpret relativity as merely prohibiting "signalling" or the transmission of "information". Those are curious, human-centric concepts, and relativity is supposed to be about the fundamental structure of space-time. A clean example here, that helps make this point, is Bohmian Mechanics. It, like orthodox QM, doesn't support superluminal signalling. Yet the theory is (I submit) as blatantly inconsistent with relativity as anything could be -- it requires a preferred foliation of spacetime for its unambiguous definition. That should help you see why it isn't "signalling" (or any such thing) that matters. I will also note that orthodox QM, just like Bohm's theory, also requires a preferred foliation of space-time for its unambiguous definition. This, as I think you'll appreciate, has to do with the collapse postulate and not the "ordinary" (e.g., Schroedinger) dynamics. So the fact that the ordinary dynamics can be made relativistic (as in the Dirac theory, or QFT) doesn't actually produce a relativistic theories. Those allegedly-relativistic generalizations of QM *still require measurement axioms* (the projection postulate) if they are going to make the right predictions for experiments. And those extra postulates require extra, anti-relativistic spacetime structure. This is why lots of half-sensible people who want to reconcile QM with relativity now all believe in the many worlds interpretation -- which is essentially nothing but the orthodox theory sans measurement axioms. So it is indeed consistent with relativity in a way that (say) orthodox QFT actually is not. Of course, it's also crazy. (Hence "half-sensible"!) I think probably all of this is too advanced and technical for this thread, though. Maybe you can email me privately and we can discuss these things without scaring the natvies? It's actually a complete myth that Bell's theorem says anything one way or the other about hidden variable theories (which I'm assuming is why you raise this). Local hidden variable theories fail to be empirically viable for precisely the same reason local non-hidden-variable-theories so fail -- namely, they are local! And non-local hidden variable theories are hardly "extremely speculative". There's a really good, plausible, physically sensible, and empirically adequate one that's been around in some form since before Heisenberg cooked up matrix mechanics. I speak of course of the de Broglie - Bohm "pilot wave" theory. You say that theories of this type would violate relativity. That's true, they do. But what Bell proved is that any empirically viable theory has to violate relativity (well, more precisely, has to include the kind of non-local causation that everyone has believed all these decades entails a conflict with relativity). Which makes the non-locality of Bohmian Mechanics a feature, not a flaw. I agree with your statement about what's naive, but I think we would disagree about the extent to which you can genuinely get classical mechanics out of an "unprofessionally vague and ambiguous" theory like orthodox QM. (That was Bell's characterization of the theory, and I agree.)

I don't think I know what you mean by "alternative" here. Alternative to what? If you mean Bohm's theory (considered as an alternative to TEW?) then check out the encyclopedia article I linked to previously, and follow any references that look interesting. David Albert's book "Quantum Mechanics and Experience" is a nice introduction to the various alternative theories for understanding this stuff and includes a nice chapter on Bohm's theory. (There was also a nice Scientific American article by him in, I think, 1994 with the title "Bohm's Alternative to Quantum Mechanics.") If, as I said before, you just want to understand Bell's work and its relation to relativistic locality, you can't beat Maudlin's book "Quantum Non-Locality and Relativity". Hope that helps.

I don't think it would be worth the time to write a condensed version for a general (non-Objectivist) audience. The fact is, there are only two categories of people who might ever be remotely interested in this book. The first category is people includes the followers of Robert Prechter, the book's publisher. He is, as far as I can tell, a fellow crackpot from a different field, and I have not the slightest reason to care that a bunch of his followers are apparently wasting their money on a book they will never read (to pump up its sales for, I guess, the alleged good of whatever crazy movement these people think they are part of). The second category of people includes Objectivists who have heard from other Objectivists that Little is an Objectivist and that his theory is revolutionary and important and good and perhaps true. I do have some reason to care about these people, but I think my post here on OO.net (plus, you know, the grapevine) will be sufficient to reach any such people who are reachable. What I am saying is, outside of Objectivism, there is no point trying to dissuade people from buying the book. Because outside of Objectivism, no serious people will have even the slightest possible reason to consider buying it in the first place. Making a big fuss out in the general public about how terrible it is, will only give it undeserved attention.

I want to respond to some things that were posted at Betsy Speicher's "Forum 4 Ayn Rand Fans". (Link) First, Betsy wrote that I have "been opposed to the TEW for years because support... a competing theory." Both conjuncts are true, but their conjunction with "because" is false. I have opposed the TEW for years. And I do support a competing theory (namely Bohmian Mechanics). But I do not oppose TEW *because* I support Bohm's theory. Even if Bohm's theory didn't exist, I would oppose TEW. This is because the grounds for rejecting TEW -- namely, that Bell's theorem and the associated experiments prove conclusively that no local theory such as TEW can make the correct predictions for the experiments -- has absolutely nothing to do with Bohm's theory. Trying to be as charitable as possible, however, I can see why someone might get the impression from what I wrote above that these two issues are connected. But let's be clear. The only reason I discuss Bohm's theory in my critique of Little's book is that Little's presentation of Bohm's ideas is the smear job of a dishonest and ignorant hack. So I was attempting simultaneously to defend Bohm's views from the unfair criticisms and explain why TEW is wrong. But maybe I could have done a better job of separating those two tasks. Second, someone named JeffT "glanced" at my essay. He "didn't read the bulk of it, but ... skimmed through the conclusion to see if there would be any justification for the character attacks in the opening." As anyone who actually took the time to read my whole essay would know, the "bulk of it" does indeed contain justification for everything I say in the opening and closing. But let me briefly elaborate on something I mentioned only in passing at the beginning of the essay: the behavior of Little and his supporters in internet debates about these issues in the late 90's and early 00's. Several people, including Al Tino, Eric Dennis, and myself, repeatedly and exhaustively explained to Little and his supporters why there was a serious problem with his theory vis a vis Bell's theorem. He eventually retracted that aspect of his 1996 paper. In the several following years, he put forward several attempts to "fix" that aspect of the theory. Each of these was also eventually retracted. So it is 100% certain that Little (and any of his more educated supporters) knew that this was a serious problem. As I explained in my essay, I thought for sure that Little would come up with some new (ultimately unviable, but, I thought, maybe at least clever and novel) attempt to reconcile his theory with these EPR-Bell experiments, during the half-dozen or so years that he was, presumably, working in relative seclusion on this book. But as it turns out the book contains no attempt whatsoever to deal with these problems. What does that mean? I can only assume it means that he worked hard to reconcile his theory with these experiments, discovered (finally) that it couldn't be done, and so simply evaded the whole issue, i.e., swept the problem under the rug. That is not honest. And there is no other explanation for his behavior. Let me also clarify something about the relation of Bell's theorem to TEW. I have said several times that Bell's theorem (plus the results of the associated experiments) prove that no locally causal theory can be empirically viable -- that is, no theory respecting relativity's prohibition on superluminal causation can correctly account for what is observed in these experiments. What is the relation of this fact to the fact that TEW is false? Well, it is a simple deduction from "no local theory can make the right predictions for these experiments" and "TEW is supposed to be a local theory" to "TEW doesn't make the right predictions for these experiments." And it is certainly helpful to know about Bell's theorem in order to understand that the problem with TEW is *not* merely that nobody has yet figured out how to account for these particular experiments using the theory. What Bell's theorem proves is that it's hopeless. But note that you don't *have* to infer the empirical unviability of TEW from this deductive argument. It would be more direct, and in some ways clearer, to just look at what TEW's actual predictions for the experiment *are* and just *see* whether they agree with the data or not. So why don't we do that? Because TEW isn't really a serious theory, it's just a half-baked qualitative idea. It doesn't actually *make* any definite predictions for how these experiments should come out. Several of its now-retracted versions have made such predictions, but those predictions were all either wrong or snuck in an assumption of nonlocal causation. That, of course, is no surprise to anyone who understands Bell's theorem. But it is a nice way of framing the problem for anyone who thinks maybe TEW should still be supported. I'll phrase it as a direct challenge to Little or any of his supporters: what is TEW's prediction for these experiments? How exactly are we supposed to calculate the correlation coefficients according to TEW? Stop with the polemics (against Bell, against Bohm, etc.) and just explain how to understand these experiments from the point of view of TEW and what precisely its predictions are. I'll even put my money where my mouth is. I will bet anyone a thousand dollars that, if Little or one of his supporters addresses that challenge head-on and explains precisely how to calculate the predictions for these experiments using TEW, it will turn out either that the predictions are empirically wrong, or that the explanation is not actually local. (I'd like to bet a billion dollars, actually, but then nobody would take this as a serious wager, which in fact it is.) How can I be so certain? Because this is precisely what Bell's theorem proves: theories that make the right predictions for these experiments *have* to utilize nonlocal causation. Those that don't will necessarily make the *wrong* predictions. So... any takers? Finally, another poster at that other website (ruveyn ben yosef) makes what would be, in a different context, a perfectly reasonable and level-headed point: "In criticizing what purports to be a scientific theory character judments [sic] have no part. One addresses the theory and only the theory with contraindicating facts." That is true, up to a point. For TEW that point was reached many, many years ago. That is: I and many other people took exactly this approach to Little and TEW for several years. Little and his supporters have never responded in an appropriately scientific way, namely, by owning up to the problems and reconciling their beliefs with the facts. They have instead resorted to massive evasion, ad hominem, distracting polemical rhetoric, and burying their heads in the sand. That is why my essay is not directed at Little at all, but to his innocent possible victims (which actually includes anyone who cares about Objectivism and doesn't want to see it slandered by association with dishonest crackpot garbage). I no longer consider Little (or his non-ignorant supporters) worthy of any attempt at civil scientific dialogue. Nevertheless, as I have said, I would be happy to elaborate in further detail, to anyone who cares enough to ask and right here in public, any of the points I made in the essay.

Sure. No, I think you were reconciling metaphysics with what some other people (be they physicists or philosophers, amateur or professional, or *whatever*) *take* to be the physics. My point is that, whoever they are, they haven't got the physics right. So there is no such question of how to reconcile "the physics" with metaphysics. But this is enough off topic that it's probably not worth pursuing, at least here. For what it's worth, that 1951 book of Bohm's is a classic quantum text. But it's a classic because it's a very good presentation of the "orthodox" views that Bohm, in 1951, still accepted and was trying to understand more deeply. It is no coincidence that in the following year, 1952, Bohm came out with his revolutionary new approach to quantum physics -- which actually turns out not to have been so novel, because de Broglie had more or less presented the same theory in 1927 but given it up under peer pressure from the orthodox establishment. My point is, if you want to understand the "Bohm's theory" (aka Bohmian Mechanics, aka Pilot Wave Theory, aka the de Broglie - Bohm theory) I mention in the essay above, Bohm's 1951 book is certainly not the place to look. Probably the best first place to look is the following online encyclopedia entry: http://plato.stanford.edu/entries/qm-bohm and then follow the references. If you or anyone else wants to understand Bell's theorem and all the associated issues (like the EPR argument, the implications vis a vis relativity theory, etc.) there is no better source than Tim Maudlin's excellent 1994 book "Quantum Non-Locality and Relativity." Actually, I take that back. There is one better source: Bell's own papers. But those are a little less accessible and definitely less pedagogical than Maudlin. And I will also warn people that this subject is highly controversial and the vast majority of commentators on this subject have got things disasterously mixed up. So if you just go to your local bookstore and grab whatever they have that covers Bell's theorem (in an apparently accessible way), you are exceedingly likely to get swindled. So, really, if you want to spend some money and time pursuing this, get Maudlin's book.

Grames, you're welcome. I'm happy to have saved you some time. I should maybe say, though, that I don't think there's anything wrong with reading the TEW book or his earlier paper. The point, really, is that if you do read them, you shouldn't go into with the attitude "What's wrong with physicists that they don't see the brilliance of this?" but rather "What's wrong with this?" As to your "own modest crackpot attempt to rationalize..." I agree with some of your conclusions (for example, that treating electrons as point particles "is an approximation of convenience"), but not exactly with the reasoning. I don't see this as an issue of reconciling physicists' claims with metaphysics. First off, I don't think you can validly deduce from metaphysics that, say, electrons aren't points. At least, it is too rationalistic to argue that electrons have charge density e/V (where V is their volume), so V can't be zero or else the charge density would be infinity, which isn't allowed by metaphysics. This kind of reasoning relies too heavily on a naive, classical picture of what an electron looks like, which picture is almost certainly wrong. And alternative (maybe true) pictures could be immune to that kind of reasoning -- e.g., maybe it turns out that what we call "charge" is not really a property of the particle at all, but of an associated wave which guides the particle. Or maybe an electron isn't really a particle at all, but some kind of stable topological structure in some kind of field. Or maybe something even weirder that nobody has even thought of yet. But here is the main point. Who ever claimed that the electron was a point particle in the first place? I think if you find real physicists saying this, and probe a little further, you'll find that all they ever meant was that its size is too small to be detected and/or too small to play any role in current theory. It is really the same point as that Newton's theory of gravity contains action at a distance -- it does, if you take it literally and superficially-formalistically. But if you think more deeply about what Newton was doing and why (and read his actual words on this very point) you find that Newton himself didn't believe in action-at-a-distance, nor did he think his theory committed one to it. The point is that he never intended his law of gravitation as the "final word" in gravitational theory. So one should understand the action-at-a-distance present in Newton's law of gravitation as simply an "approximation of convenience" -- i.e., one should understand it as indicating that there is something further to be learned, by some future research program, about how and how fast gravitational influences propagate. This, for what it's worth, is also precisely how one should understand the similar type of action-at-a-distance that is (again, superficially-formalistically) present in Bohm's quantum theory. It doesn't mean, as some critics have asserted, that the theory posits "truly instantaneous" nonlocal causation. Rather, it means only that there are causal influences which are too fast to be measured currently and too fast to differ meaningfully from instantaneity as far as the current context of knowledge is concerned. Do you see the relation back to your question about point particles? My point is that, whoever you are arguing with that says that physicists say electrons are really, truly points of infinite density (or whatever), doesn't really know what they are talking about. There is a (superficial-formal) sense in which this is part of current theory. But I think most physicists understand, or at least should understand, this already in precisely the way you suggested: as a contextual approximation of convenience.

I first heard of Lewis Little’s Theory of Elementary Waves (TEW) in the summer of 1996. Like many other people that I respect, I was initially very intrigued by the theory. The qualitative idea of “reverse waves” seemed like it might genuinely explain several puzzling quantum phenomena as well as the (also puzzling) fact that all observers measure light to move at the same speed, regardless of their own state of motion relative to the light’s source. But after eventually reading Little’s 1996 paper (in the fringe journal “Physics Essays”), and as my own expertise in physics developed during graduate school, and as I observed the behavior of Little and his supporters in public debates, I came to realize that TEW was certainly wrong and Lewis Little was nothing more than an ordinary (but perhaps extraordinarily dishonest) crackpot. Why, then, did I buy and read Little’s new book (“The Theory of Elementary Waves”) when I heard that it had been published? The main answer is that I thought, surely, after all these years, Little would have been able to concoct some kind of account of the EPR-Bell type experiments that had caused him so much trouble, almost a decade ago now, when these matters were being actively discussed on public internet forums. And I thought that it might be an enjoyable and perhaps even illuminating exercise to unravel the confusions and mistakes in that concoction. Sadly, and as I will discuss in further detail below, there was no such concoction. Little’s account, in the new book, of Bell’s theorem and the crucial associated experiments is so brief, so straightforward, and so obviously wrong that it leaves literally nothing, for someone who already understands these issues, to unravel or even contemplate. So my earlier judgments about this theory and its author have not been changed at all based on this new book. Actually, they have become somewhat more negative. Given all that, why am I bothering to spend my Sunday morning writing a (rather long, I expect) review of the book? The answer here is that Little has described himself as an Objectivist, and those interested in or sympathetic to the theory have been (as far as I know, exclusively) Objectivists or Objectivism-sympathizers. As an Objectivist myself, I want to go on record as saying that (and explaining in detail why) TEW is crackpot garbage which (despite Little’s occasionally plagiarizing sentences from Rand or paragraphs from Peikoff in the book) has nothing to do with Rand or Objectivism, should not be supported by Objectivists, and should not be shared with respectable scientists (including students) under an Objectivist banner. This last is especially crucial: we who understand and appreciate Objectivism, and want to see it become more widely understood and appreciated in the culture, should never work to associate it, in the minds of our potential audience, with dishonest crackpot garbage. Finally, I suspect there are students who, not knowing enough physics to know better, but perceiving that Little spouts Objectivist slogans, might be fooled into thinking that it is worth taking the theory seriously and working to better understand it. My hope is that this review will save some such good people some wasted time, by helping them understand the theory’s true nature. This review will not aim to provide a systematic summary of the contents of the book. I will mostly focus on the book’s sixth chapter (“Bell’s theorem”) which provides the easiest foothold to establish the overall viability of Little’s project. But I will make several overall remarks about the book first. AUDIENCE It is very curious, and was certainly a surprise to me when the book arrived, that Little has chosen to present his allegedly revolutionary new theory of physics to a lay audience. There is, of course, nothing wrong with that in principle. But if Little genuinely thought his ideas were correct and wanted to convince others of this fact, he should write for people who are at least capable of having a legitimate opinion about these matters, i.e., for an audience with at least some minimal training in physics. That he has chosen not to do so is very revealing. Presumably Little would explain his decision to write for a lay audience by claiming that all well-trained physicists are so steeped in irrational methodology and false ideas that they couldn’t understand or appreciate his alternative views, or at least wouldn’t allow his work to be accepted in peer reviewed journals. But that, simply, is not true. There are whole journals, even respectable ones (like “Foundations of Physics”, whose editor is a recent Nobel prize winner) which specialize in deep, often critical, analysis of the conceptual foundations of QM and Relativity. Little is right that the physics culture overall is rather hostile to such things as finding causal explanations for the formalism of QM, and, in general, to deep, critical analysis of the conceptual foundations of modern physics. But there do exists rather large and entirely respectable pockets of rationality (meaning groups of individuals who pursue this kind of research, and entire journals devoted to it) to which Little, properly, ought to address his arguments. Or more precisely: should have (and would have) addressed his arguments -- if he genuinely believed that people who are well-trained in physics (but also sympathetic to foundational criticisms of modern theories) could be persuaded by them. So, in the end, it is indeed profoundly revealing that Little has chosen to address those without any training in physics. My reason for making this point is not, however, mainly to impugn Little’s honesty or motives. It is rather to raise a certain question in the minds of the lay audience for whom Little writes: if you are untrained in physics (and hence unqualified to judge the truth of Little’s claims), why does he address himself *exclusively* to you? A useful comparison here might be a doctor who wanted to sell you his revolutionary new cure for cancer, but who wouldn’t or couldn’t publish the details of his ideas in actual medical journals. If the product is so wonderful, why would its creator waste his time trying to convince *you*? (This is, I hope it is clear, no criticism of you. Rational people who aren't experts in a given field understand that they can't accurately judge controversial matters in that field and hence don't *expect* to be the audience for controversial new ideas.) Note also here that physics is relevantly different from philosophy. The subject matter of philosophy is, by definition, that which is accessible to any person in any era. No special training is required to understand philosophical issues and judge the veracity of philosophical theories. So it could be entirely reasonable and appropriate for someone with a revolutionary new approach to philosophy to address him- (or her-) self primary to an audience of non-professional-philosophers. This is not true for physics. POLEMICS Little’s book is very polemical. He often, on a given topic, spends more time criticizing his alleged opponents than he does presenting and clarifying his own theory. Although this is somewhat disappointing and distracting, there is nothing in principle wrong with polemics – especially against the orthodox understanding of QM, which indeed deserves to be criticized. What is wrong, though, is that Little’s polemics are *sloppy* and *biased* in a way that repeatedly undermines his own positive case and in a way that reveals him to be, at best, negligently ignorant of that which he criticizes. He tends in particular to package together everything that is definitely wrong, everything that is conceivably dubious about any of the (several) theories he opposes, and several other ideas which turn out to be true, into one allegedly-monolithic opponent. For example, a layman reading his book will get the impression that the “standard quantum theory” he opposes includes all of the following theses: (a) physics is all about equations that work, not about providing clear physical descriptions of underlying mechanisms, ( human consciousness is causally operative in measurements involving microscopic objects such that, e.g., the moon isn’t there when nobody looks, © backwards-in-time causal influences exist, (d) faster-than-light causal influences exist, etc. But there is probably no single person who endorses all of these ideas. (a) is indeed part of the orthodox quantum philosophy, but it is strongly rejected by those who favor, for example, Bohm’s theory, the GRW theory, or even the Many Worlds theory. Hardly anybody believes ( – it is a fringe idea advocated by a couple of well-known people (like Wigner) over the decades, but none of quantum’s founding fathers (Bohr, Heisenberg, etc.) actually believed it, and hardly anybody takes it seriously today. Same with ©. And people who (as we will see later, correctly) interpret Bell’s theorem and the associated experiments as proving (d) – including Bell himself – are considered a crackpot fringe by the vast majority of physicists, who instead typically (and wrongly) interpret Bell’s theorem to establish the failure of determinism. Little’s polemical packaging of the orthodox Copenhagen philosophy of quantum mechanics with Bohm’s theory is particularly troubling, not only because these two approaches to quantum theory could hardly be more different, but also because Bohm’s theory actually accomplishes all of the virtues that Little claims for his own theory in the first five chapters of the book. Little’s packaging of these is apparently based on his belief that the nonlocal causation posited by Bohm’s theory is just another type of the same basic “magic” posited by the Copenhagen theory. What he doesn’t seem to understand about Bohm’s theory, though, is that this allegedly “magical” non-local causation only arises in situations involving two or more specially-prepared (technically, “entangled”) particles. But as long as one is talking about situations involving a single particle -- and that is all Little does talk about before his chapter 6 -- Bohm’s description of the physics is entirely local and (more generally) acceptable by all of the standards Little endorses in these chapters. Here’s an example. On page 13, discussing the double slit experiment, Little writes that “modern physicists .... maintain that a particle’s motion is affected not merely by interaction with the wave in the ‘local’ environment of the particle, but in addition through a ‘nonlocal’ interaction between the particle and every portion of the wave … throughout its entire extent in the greater environment of the particle.” First off, this is certainly *not* something maintained by the typical or majority “modern physicist” – they don’t even accept that there are two distinct (and hence possibly interacting) entities, a wave and a particle, at play here. Little’s description must therefore be intended as a description of Bohm’s theory, which is the only extant theory which posits genuine particles being influenced by distinct waves. But not only do “modern physicists” not widely accept Bohm’s theory -- what Little says is not even true of Bohm’s theory. According to that theory, and (again) as long as we are just talking about a single particle, the particle is influenced *exclusively* by the properties of the wave *at the location of the particle*. There simply is no nonlocal causation in Bohm’s explanation for the result of the double slit experiment, or any of the other experiments discussed by Little in this first part of his book. At the end of chapter 4, Little summarizes what he has been arguing for as follows: “Again, in every case, the result obtained is exactly what quantum mechanics predicts and exactly what is in fact observed in the laboratory. At no time does the particle photon exist in multiple states – an alleged ‘superposition of states.’ The wave splits into two waves and takes both routes through the [apparatus]: the particle takes only one route or the other. The whole notion of some new measurements theory simply evaporates.” This echoes a similar comment (from page 31): “The theory clearly explains, at least in principle, the process by which individual particles reach the screen, a process that involves no nonlocality.” Little’s overall point is that, by positing both a particle and a wave, TEW is able to explain all of these one-particle experiments in a way that is deterministic, comprehensible, and local – i.e., in a way that doesn’t rely on what Little calls “magic.” My point here is simply that, to whatever extent anyone finds any of this illuminating and promising, they need to look into Bohm’s theory, which provides an explanation for all these experiments with all of the same virtues Little claims for TEW (including the lack of nonlocality). Little's sloppy and biased presentation, however, would never convey to an honest reader that this was the case. Instead, an honest layman would get the false impression from these chapters that TEW is uniquely (and, in particular, as opposed to Bohm's theory) able to account for the results of these experiments in a sensible way. NONLOCALITY That brings us to the key issue. If one is going to prefer TEW to Bohm’s theory, that preference could only be based on the fact that, in situations involving two or more entangled particles, Bohm’s theory includes nonlocal causation, while TEW does not. So the key question is going to be whether nonlocal causation (of the sort posited in this kind of situation by Bohm’s theory) is real, i.e., whether positing it is a necessary condition for a theory to be empirically adequate. This is precisely the question addressed by Bell’s theorem and the associated experiments, which is the subject of Little’s chapter 6. There are many, many wrong and confused statements in this chapter. A complete post-mortem would require significantly more time than I am willing to dedicate to this project. I will instead just focus on what is really central – Little’s claim that his theory is immune to Bell’s theorem, which claim is the culmination of the discussion on pages 71-72. To begin with, Little is adamant that, in TEW, the two photons involved in (each run of) this experiment contain what physicists call “hidden variables” which determine how each of them will respond to a polarization measurement along any arbitrary direction. He writes, for example: “In fact, the two particle source determines everything. The manner in which each photon will act at its polarizer, for any orientation of the polarizer, is determined upon emission of the photon pair at the particle source, and thus while the two photons are still together at the same location.” And further: “Each individual photon would, of course, have to carry parameters of some sort that would cause the photon to act one way or the other – vertical or horizontal – at its polarizer.” Now, as anyone familiar with Bell’s theorem would surely know, this is *precisely* the type of theory that must, as established by the theorem, make the *wrong* predictions for the relevant experiments. It is at this point that I was expecting some novel story of photon particles hopping from one wave to another as the polarizers are rotated – the sort of story Little concocted several versions of years ago, before finally being made to understand that none of them worked. He subsequently removed himself from public discussion of his theory, and went, I presumed, back to the drawing board. I thought for sure this book would include some results of that (drawing board) work -- some clever new account, the identification of the errors in which would make for a pleasant bit of work over my Sunday morning coffee. But instead, we get the following patent nonsense: “But these parameters would not be the equivalent of the hidden variables whose existence is refuted by Bell’s theorem. Quantum mechanics, even assuming nonlocal interactions, does not predict what the polarization of each individual photon will be. Instead it predicts the probability of one outcome or the other. The probabilities vary as one varies the orientation of the polarizer. But the variation in the probabilities occurs in a smooth, continuous manner. Bell’s theorem proves that no such smoothly varying probability distribution, applied at each polarizer, could possibly account for the observed correlations unless there is interaction between the two sides. In the TEW picture, no such smoothly varying distribution is conveyed to the polarizers. What the photons do convey is a simple yes or no – vertical or horizontal – for each polarizer orientation. This distribution is totally discontinuous. Bell’s theorem does not apply.” As something of an expert on Bell’s theorem, I have seen (and even diagnosed, in refereed journals) many mistakes made by commentators on Bell’s theorem. But this is, without a doubt, the first time I’ve ever seen the claim that Bell’s theorem applies *only* to theories that are, like orthodox QM, non-deterministic. In fact, determinism is no part of the arguments leading to Bell’s conclusion, though the way those arguments are sometimes (and, in textbooks, usually) presented does make it look a little bit like the arguments are premised on determinism. So the usual misunderstanding is at least comprehensible. But I truly have no idea where Little got this opposite misunderstanding: that Bell’s arguments are premised on *indeterminism* such that the theorem would simply fail to apply to TEW. It is truly a bizarre claim that nobody with the slightest familiarity with Bell’s theorem, Bell’s actual papers, or even the copious (and so often misleading) secondary literature, could possibly make. If Little is actually this confused, he has no business writing this kind of chapter or this kind of book. (And, anyway, he has no business being this confused after so many years back at the drawing board, after having been made acutely aware that Bell's theorem was a serious problem for his theory.) And if he’s not actually this confused, then what he says here can only be understood as a deliberately dishonest attempt to evade a fatal flaw in his theory, and swindle innocent and ignorant readers. But let us leave that aside and simply take Little at his word – that, according to his theory, “Each and every potential polarization of each photon is determined at the source.” And, further, that “Delayed rotation of a polarizer is also of no significance. Whatever the orientation of a polarizer when a photon arrives, the polarizer measures the previously determined polarization accordingly.” Following Bell, let’s work through the implications of these claims for the relevant sort of experiment. First, we need to get straight on some terminology. Suppose there are two experimenters, Alice and Bob, who will each measure the polarization of one of the photons from the pair along some direction. In particular, Alice will choose (randomly, or using free will, and at the last possible second) to measure the polarization of her photon either along an axis we may denote a or another axis we may denote a’. Bob, similarly, will measure along either the axis b or b’. Now TEW claims that each particle pair is created, at the source, such that every possible polarization measurement on either of the two photons is determined. We may thus introduce the following mathematical functions to describe those encoded outcomes: A(a,L) represents the pre-determined outcome of Alice’s experiment in the case that she measures along axis a; A(a’,L) represents the pre-determined outcome of Alice’s experiment in the case that she measures along axis a’; B(b,L) represents the pre-determined outcome of Bob’s experiment in the case that he measures along axis b; and B(b’,L) represents the pre-determined outcome of Bob’s experiment in the case that he measures along axis b’. The L in all of these formulas refers to the set of “hidden variables” or “source parameters” or whatever it is (variables carried by the particles, something determined at and existing at the particle source, or whatever you like) that is the physical cause of the outcomes. Notice that this L will presumably be different for different pairs of particles – that is, not every pair will respond to every possible measurement the same way (because the hidden variables or source parameters or whatever are different from run to run) so we allow for this by conditionalizing each of the functions expressing the pre-determined outcomes on the particular relevant facts about the state of the pair (whatever exactly those are). In effect, we are introducing four functions for each possible such state of the pair. Let us also, for convenience, stipulate that the functions A and B take on values +1 and -1 (representing, respectively) “vertical” and “horizontal” polarization along the specified axis. Then everything is in place for the following theorem (which is a well-known modern updating of Bell’s original theorem). Consider the quantity s defined as follows: s = A(a,L) B(b,L) – A(a,L) B(b’,L) + A(a’,L) B(b,L) + A(a’,L) B(b’,L) which tells us something about how the different possible outcomes encoded (at the source) into a given particle pair are related. We may then algebraically re-write s as follows: s = A(a,L) [ B(b,L) – B(b’,L) ] + A(a’,L) [ B(b,L) + B(b’,L) ] Now consider the two terms in square brackets. Since the two B functions take values either +1 or -1, one or the other of these two terms will always be zero. The way to see this is follows. Either B(b,L) and B(b’,L) are the same, or they are different. If they are the same, then when we subtract them (as in the first term in square brackets) the result is zero. If they are different, then when we add them (as in the second term in square brackets) the result is zero. Furthermore, whichever term in square brackets is *not* zero will equal either +2 or -2. And so, when that term is multiplied by A(a,L) or A(a’,L), each of which is also equal to either +1 or -1, the overall result will necessarily be either +2 or -2. Thus, s itself is always equal to either +2 or -2. And so the average value (over lots and lots of pairs with different values of L) of the absolute value of s will necessarily be less than 2. That, as it turns out, is all there is to Bell’s theorem. The only remaining puzzle is how this relates to the experiments. But this is pretty simple, too. The experiments choose (remember, at random) some particular pair of axes (a and b, or a and b’, or a’ and b, or a’ and b’) along which to measure the polarizations of the two photons in a pair. From the results of the subset of the runs in which a given pair of axes was measured along, the experiments can compute a correlation coefficient – e.g., C(a, = [N(VV) + N(HH) – N(VH) – N(HV)]/N Where N(VV) is the number of the runs in which both outcomes were “vertical”, etc., and N = N(VV) + N(HH) + N(VH) + N(HV) is the total number of runs of that type. In slightly simpler terms, C(a, is just the fraction of times, for polarizer settings a and b, when the outcomes are the same, minus the fraction of times when the outcomes are different. Such a correlation function can be computed for each pair of possible measurement axes, and a little thought reveals that each one corresponds precisely to one of the four terms in the theoretical quantity s defined above. Thus, theories of this type must predict that | C(a, – C(a,b’) + C(a’, + C(a’,b’) | < 2. This is Bell’s inequality. And the experiments uncontroversially prove that the absolute value of this combination of correlation coefficients is *not* less than 2. In fact it is about 40% bigger than 2. In other words, the actual experiments are not even close to the predictions that a theory of the TEW type must make. So much for Little’s claim that Bell’s theorem simply doesn’t apply to TEW. WHAT BELL’S THEOREM ACTUALLY PROVES The question of what Bell’s theorem and the associated experiments actually prove is subtle, and I have written extensively on this elsewhere. Suffice it here to say that, despite what one often sees in the secondary Bell literature, it is not determinism or hidden variables (or reality) that are refuted – it is the idea (which is usually considered an implication of relativity theory) that causal influences can never propagate faster than the speed of light. That is, what Bell’s theorem and the associated experiments prove is the real existence of “nonlocality.” (And please take those last two sentences as a stipulation about how I am using the word “nonlocality.”) Little calls nonlocality “magic” and therefore packages it together with other dubious claims of orthodox QM and its adherents. This is completely wrong. The only possible basis for opposition to faster-than-light causation is relativity theory. And however strong one thinks the evidence in favor of relativity is or was, its turning out to be false (or not-quite-right in some slightly more subtle way) would not mean the acceptance of “magic.” Little’s polemical rhetoric here is sloppy and dishonest. What I want to come back to here, though, is TEW vs. Bohm’s theory. Bohm’s theory has all the virtues Little claims for TEW in situations involving single particles. And Bohm’s theory has the additional virtue of making the correct prediction for these EPR-Bell type experiments – which it is able to do precisely because it includes the sort of nonlocality that Bell proved must be a feature of any such empirically viable theory. On what reasonable grounds, then, could one possibly think that TEW is superior to Bohm’s theory? There are none. CRACKPOTTERY Actually all of this discussion has been far too generous to TEW. I have made it sound like TEW is a legitimate physics theory, which can be compared and contrasted to other legitimate theories like Bohm’s. This is really not the case. Bohm’s theory is well defined by a clear posited ontology and a set of precise mathematical equations that define how the physical objects posited in the ontology act and interact. TEW is, by contrast, a vague half-baked idea. There is no clear posited ontology (at a level of precision beyond the vague talk of different kinds of particles and different kinds of elementary waves), and there is certainly no precise mathematical account of how these various objects act and interact. There is only loose talk about how everything is exactly the same as standard theory. But that is really not good enough, and there are many – I repeat, many – situations (including several discussed in detail in the book) in which it is quite clear to this professional physicist, at least, that TEW is *not* going to make the same (correct) predictions as standard theory. (The EPR-Bell case is just the most dramatic and most clear-cut example.) This is the beginning of the rationale for describing TEW not merely as a false theory, but as a crackpot theory. Crackpots are people who have only a superficial understanding of a broad field of knowledge, but who nevertheless erroneously convince themselves that they’ve revolutionized the field. Physics crackpots are very common. This may come as a surprise to people who aren’t professional physicists, but we receive unsolicited crackpot articles and books in the mail (electronic and otherwise) all the time. I have read many of these that I have been sent, just for the (perhaps not fully rational) pleasure at laughing at someone else’s rampant and typically angry and high-flown misunderstandings and confusions. The point I want to convey here is that, even beyond the serious fundamental flaws I’ve outlined already (such as being addressed to a lay audience, being inappropriately polemical, and fundamentally misrepresenting Bell’s theorem), Little’s book shares many of the other common traits of crackpot physics. It has a distinctive “the world against me” tone, which (as already discussed a little under the heading of POLEMICS) is inappropriate insofar as the rest of the world is not, in fact, monolithically against whatever element of reasonableness is present in or motivating the author’s views. It contains extensive errors that can only be described (without intending any pun) as “elementary” – see especially, for example, Little’s chapters 7 (on relativity) and 10 (on magnetism). It displays a negligent ignorance of the history of the field, including especially an ignorance of what other partly-like-minded critics and skeptics have tried before. It sets itself up as an alternative, not to the best its opponents have to offer, but to the worst. It fails to acknowledge or engage with the sorts of examples that well-trained physicists would regard as obvious counterexamples (or particularly difficult cases) for the theory, and instead engages in the sort of psychological down-hill-running that is characteristic of people who care more about being (seen to be) right than about truth. It lumps together things that deserve to be denounced (such as the idea that consciousness is somehow causally involved in the quantum measurement process) with other perfectly legitimate ideas (such as dark matter and even the magnetic field!). It alleges that certain terminology (such as “cross-product force” and “behavioral field”) is “standard” when, in fact, it isn’t – thus again evidencing unfamiliarity with the fields being criticized. It includes wild, baseless speculation about the possible application of the revolutionary new theory to such distant fields as biology and neuroscience and the philosophy of mind. And, finally, the identity of the book’s publisher does imply something about the seriousness with which it should be taken – and this is true whether Little chose this publisher or used it because it was the best he could find that would publish the book. The phrase “not even wrong”, originally attributed to Wolfgang Pauli and recently re-injected into discussions of physics by Lee Smolin’s criticisms of string theory, has recently become popular in Objectivist circles. That is a good thing in that the phrase does accurately and dramatically convey the status of ideas which fail to have the kind of (qualifiedly positive) relationship to reality that is denoted by the concept “wrong.” But it is also unfortunate, because -- in becoming widely known and so being attributed, rightly or wrongly, to all kinds of things -- the phrase has become diluted and lost some of its punch. Which is unfortunate because it is the perfect phrase for describing Lewis Little’s TEW. The theory is, truly, not even wrong. CONCLUSION If you have some reason to care about the sorts of foundational issues in physics that TEW is supposed to address, you should by all means pursue them. I would be happy to recommend some literature at the appropriate level for anyone who asks (here, or on HBL, or by private email). And if there is anything in this essay that you can’t follow or don’t understand or would like further elaboration or examples of or if there's something from the book that you'd like some help understanding the problems with (if any), I would also be happy, within reason, to try to oblige. An open and transparent discussion can only work in the favor of truth. I ask, however, in repayment for the time I have invested in writing this review (and the time I will presumably invest in answering questions subsequently), that you respect some reasonable guidelines. If you don’t have enough knowledge to, or don’t have the time or motivation to, engage in serious discussion of these issues, please do not proselytize for (or even mention) TEW to your friends, to your professors, or to people on the internet, or to anyone – especially in a context where you would convey to your audience that there is some connection or affiliation between TEW and Objectivism. TEW is, in fact, an embarrassment to Objectivism. So I will close by saying the one positive thing about Lewis Little’s book that it is possible to say: it is a very good thing that there is no explicit mention of Ayn Rand or Objectivism anywhere in the book.

I think I understood what you wrote just fine. The notion (of the importance, vis a vis "certainty") of "sufficiency of evidence" was the primary view I spoke in favor of. So what you said is indeed that my views are destructive... But forget it. The reason I don't want to discuss this further is emphatically not that I'm "personally affronted" by what you said. You obviously didn't intend the comments personally, and I didn't take them that way. The reason is just that there are many, many confusions (and contortions of Objectivism) in your post, which, it is clear to me, would take a long long time to identify and unravel. And I don't have time for that kind of discussion. Again, just to be clear: the reason I quoted your bit about "destructive to rational epistemology" was not to accuse you of accusing me of something. I hate it when people initiate -- or escalate -- this kind of "you were irrationally rude in accusing me of X" nonsense in these discussions. Discussions of this kind almost always center around disagreements, and there needn't be anything personal or insulting about this. (Incidentally, here is a point -- perhaps the only one in many many years -- where I agree with Betsy about something: many of the remarks made on her website in criticism of LP's infamous comments about the last big election were perfectly reasonable expressions of disagreement with certain aspects of those comments. I find very dubious the people who go out of their way to interpret these as "vicious attacks" and thereby convert a discussion of ideas into pressure group warfare about who "dissed" whom.) So please don't get me wrong. I'm not at all annoyed or offended, nor do I feel like you dissed me, nor do I want anybody to step in and argue that I should be treated with more respect, etc., etc. (I have way more respect for people who are willing to say what they think, even when it involves open disagreement, but who remain open to improved understanding via further debate/discussion.) And hopefully you will feel the same way when I say: instead, the reason I don't want to discuss it further is that I think you badly misunderstand certain core aspects of Objectivist epistemology, and that will make any subsequent discussion too involved and too long.

I have the sense that discussing this further (to the point of coming to agreement) would be a major undertaking that I don't have time for. So I will let my previous statements stand without further elaboration, and simply register that I strongly but respectfully disagree with much of what was said in David's post -- and in particular with the assertion that my views are "destructive of a rational epistemology". I would, however, second David's suggestion that interested people might benefit from a careful study of OPAR.

I don't think that formulation is correct. It suggests that we start with hypothetical conclusions which we entirely doubt, then slowly whittle away our doubt until none remains, at which point we are certain of the conclusion. But the gaining of knowledge is fundamentally the achievement of a positive, not the removal of a negative. What the evidentiary continuum is fundamentally about is simply the fact that certain complex ideas require complex, multi-step validations. The evidence needed to establish the conclusion has to be assembled and organized, piece by piece. The evidentiary continuum designates the various intermediate stages of this development. It is true that, prior to achieving certainty, there are typically some rational empirical grounds for doubt. But to define certainty (and the rest of the continuum) in terms of (amount of remaining) doubt is, I think, to define it in terms of a non-essential. This is also misleading. Certainty is definitely about both "quantity" and "proportion" (though "total count of bits" isn't quite the right way to describe the "quantity" aspect). As noted previously, it's possible for 100% of the evidence to point toward a certain conclusion, yet for that body of evidence to be insufficient to establish the conclusion, i.e., for that body of evidence to fail to fulfill the relevant standard of proof. Conceptualizing certainty merely in terms of the "proportion of evidence" (without regard to the sufficiency of evidence vis a vis the relevant standard) makes certainty subjective, and would lead, in practice, to systematic premature claims to certainty -- i.e., systematically finding oneself in the position of having claimed certainty about things that turn out to be wrong.

This is a bit of an aside, but maybe a more important and interesting topic than what's wrong with Betsy's ideas about certainty. Dan Edge wrote: I think there are some problems here, along the same lines as post #16. First, I sense the view that the phrase "within the specified context" is being treated here as a qualification of "certainty". It isn't, and this view leads immediately back to some kind of Betsy-like distinction between two distinct concepts ("contextual certainty" vs "absolute certainty"). But all knowledge is contextual. There's no such thing as knowledge or certainty which isn't "within [some] specified context." "Contextual certainty" is just a perhaps-helpful name for plain old regular certainty, the only kind there is. (Just like: by "objective reality" we don't mean some other alternative to "regular reality".) Second, I don't understand why Dan wrote that the conclusion is "absolute within the specified context" rather than "certain within the specified context." Perhaps just a typo. Third, for a conclusion which was previously genuinely certain to be overturned when new evidence is found, is an extremely unusual situation. Dan's phrasing makes it sound like this is a normal occurrence whenever new evidence is found. If it is normal for some person to be constantly revising claims (earlier held as certainties) when new evidence comes in, that just shows that that person is using the wrong standards of proof. Fourth, I think it's flat wrong to ever say that a false conclusion "is still true given the original context." Certainty may be contextual, but truth -- correspondence with reality -- is just truth. It is a bizarre perversion of language (and thought) to describe a conclusion which contradicts the facts as (any flavor of) "truth". One of my old philosophy professors (I can't remember which) made up the following parallel to dramatize this point: if a doctor does everything right but the patient still dies, would you describe that patient as "contextually alive"? And so, fifth, I think Dan is misinterpreting the blood types example from OPAR. I have some questions about this passage, too, and think it could have been made more clear, but I think it's definitely wrong to read it as endorsing any such idea as "contextual truth." Rather, I believe the point is that the original claim (properly understood) is true. That is: the causal factors referred to by "A", "B", etc., do, even in light of the new information, have the compatibility relations that were originally claimed. It's really the same as another example LP mentions elsewhere: that gravity exerts a force which pulls heavy things down toward the earth is, and remains, true, even after one learns about airplanes. In both cases, there's nothing in the original claims (which are about certain causal factors) precluding the existence of other factors entering and yielding surprising outcomes. (By contrast , if the original claim had been "Patients with A blood will never suffer any kind of fatal blood coagulation when injected with A blood from another person" that would be refuted by the "new evidence" -- but that is a very different claim, one which would require different/stronger evidence to support in the first place. In any case, if someone did erroneously accept that claim -- even, implausibly, if he did so without any epistemological culpability -- and then learned about the possibility of rh-based coagulation, he'd have to say that his earlier claim was false -- not "contextually true", but just plain false.)

I had only really looked carefully at the descriptions of C1/C2 that were quoted in post #1 of this thread. (I haven't looked at any of earlier thread where, I gather, she offered this distinction as a route to some kind of skepticism about moral judgments.) In any case, I definitely agree with your analysis in post #28.