I sure as hell don't know what is really going on with all of that.
There, is that better? No, I'm not a neutrino expert, and I certainly haven't spent a lot of time studying tachyons, given that up until now there hasn't been any real experimental evidence that they exist (and the jury is still out on whether the current evidence is "real"). I was just kidding around with the neutrinos, as well because I am no neutrino expert. When I went to grad school neutrinos were believed to (maybe) be massless! As for trusting me about the GME -- who asked you to? Read the papers!
In the meantime, yeah, if the neutrino result pans out I suspect that I won't be the only person going back to learn or refresh memory of the consequences of that great range of trajectories outside of the light cone. In my case, one of the puzzles will be trying to reconcile the result with a presentation I attended back in the 80's (at a lunch seminar in our theory group) where a very reputable physicist argued that there must be a upper bound speed that is the same for everything, not just light, on grounds that were somewhat different from the usual relativity arguments. Unfortunately, I have no memory of whether or not it was ever published, and obviously don't remember enough to know if it was persuasive or correct. But I do think that it is safe to say that it will have some fairly profound consequences in LOTS of places...
Piffle. This is the sort of nonsense that makes people thing quantum theory is crazy or, worse, inconsistent. The very sentence is you use to state this is self-contradictory and hence meaningless. If one has perfect knowledge of the wavefunction and its time evolution, then one cannot "only probabilistically describe its behavior".
What you mean to say -- I suspect -- is that the outcome of certain measurements performed on a quantum system that is initially prepared in a specific state is only predictable probablistically (where other measurements might be completely predictable). What you are neglecting is that the measuring apparatus in this case is a) not considered part of the quantum system; b) is in an unknown initial quantum state; c) is in an initial quantum state that is essentially (semi)classical, in particular is considered to be prepared independent of the system state so that the two are in an outer product (non-entangled) state as part of your initial conditions.
The correct quantum description of the full problem would a) make the measuring apparatus a part of the quantum system; b) require the whole quantum system to be in a known initial state; c) that almost certainly would not be non-entangled, if you consider time reversal invariance. In this full problem there is no indeterminacy and no probability, only time evolution of a fully specified system wavefunction.
Probability enters quantum theory only at the point of measurement, and there it is a measure of our ignorance of state, not a measure of some intrinsic entropy content in a closed quantum system.
No, I don't understand either. I just pretend to -- not a troll, just an acknowledgement that 30 years after I got MY Ph.D. (next year) and in spite of teaching quantum and publishing papers in quantum and CMP, -- I think of most physics as "something I should understand, but don't". Some things I do pretty well on. Other things, my knowledge is positively embarrassing, or would be, if I cared.
FWIW, it took me an easy decade of post-Ph.D. existence AND those many papers before I started to get semi-comfortable with quantum theory, and even now my knowledge is very subject to fluctuation, forgetfulness, and fog -- a lot more fog as I get older. Some things get clearer and make more sense, but others become even more obscure.
The amazing thing is that if you dedicate yourself to any particular problem in QM or QFT, you often CAN make a real contribution. Sometimes it takes a decade or two. Sometimes the real contribution is a very MODEST real contribution. But every now and then somebody turns out to be a Feynman, often surprising even themselves...;-)
See other replies -- one has a few references. As for entropy, that's tough. Probably E.T. Jaynes, but other than Probability Theory, the Logic of Science I don't have a good reference at my fingertips. You could try googling "information theoretic approach to statistical mechanics" and see what turns up -- the entropy as the log of the missing information arises in this approach, which in turn arises from Jaynes and the work of Richard Cox first, Claude Shannon second. It's probably in various stat mech textbooks at this point -- but I was lucky enough to take stat mech from Richard Palmer, and he taught information theory as the sound(est) axiomatic basis for stat mech from the beginning, and much older and wiser now -- I still think he was dead right.
Ah, but this means that there IS no eventual heat death of the Universe. Well, it would mean that if it weren't for the open vs closed issue. Doesn't really restrict what happens to an open Universe much...:-)
...by hacking into the corporate network of the company you want to work for and obtaining compromising material, such as uploaded video porn involving the company president and a local group of cheerleaders (female and male cheerleaders work best), the numbers of the offshore accounts of major corporate officers -- don't be tempted or distracted by this, by the way, we're trying to get a job, not get rich directly, that sort of thing. You might want to encrypt their entire customer database as well with a key Only You Know. After this, a subtle hint in the right place -- one that just appears in their mailbox as if by magic -- should do the trick, without needing to resort to similar email messages in the mailboxes of their wives, husbands, federal agents working for the IRS, BATF, DEA and FBI. One hopes.
What, you disagree? Strange, it has always worked for me...;-)
rgb
P.S. -- and if it doesn't, well, there are always all of those account numbers...
It's no joke. Read the papers. Although if most people knowing what the hell REALLY goes on in quantum theory is a criterion for science not being in trouble, well, it's been in serious trouble for over a century now. As Feynman said, "Nobody understands Quantum Mechanics."
QM and GR (and their synthesis, fully relativistic quantum field theory) are just a bit too difficult for the human brain to fully grasp. Every decade or two a human comes along who by serendipitous chance and hard work is Einstein, Lobachevsky, Riemann, Dirac, Ramanujan, Gauss, Feynman brilliant and things advance a bit, often quite abruptly. Then we are once again stuck as we labor to overcome the flaws in what we've figured out, which sometimes require complete paradigm-shifting rearrangements of what we know. At the same time all of this is going on, new experimental evidence is constantly being produced, some of which might well reveal truly new physics, not just more about what we already know, or think we know.
We live in interesting times. Dark matter, dark energy have burst on the scene. Neutrinos have a mass. Neutrinos might go faster than the speed of light (negative mass?). The LHC has failed to find the Higgs -- again -- in a great deal of the range which -- again -- it was claimed that it would/might/should be found. Magnetic monopoles are rarely found, but never reproducibly, and hover around on the boundary of believability. Gravity remains a cruel puzzle, a deep inconsistency between quantum theory and general relativity. We still have no direct evidence concerning whether antiparticles are gravitationally attracted to particles or repelled by them! Hell, if neutrinos do have negative mass, and negative mass gravitationally repels ordinary mass, then the neutrino content of a galaxy is conceivably the missing "dark matter".
I sure as hell don't know what is really going on with all of that. One of many reasons I read/. The only way I can pay it forward is to try to post informative stuff on the little patches I've studied pretty deeply and mostly understand. I'm hell on wheels for certain kinds of Green's functions in the context of integral equation solutions to PDEs in quantum or classical field theories, not bad on quantum optics or critical phenomena or certain aspects of quantum stat mech (and generally competent in basic quantum mechanics, enough to teach it). I'm terrible wrt other stuff in physics -- it is too big, and too difficult to master it all.
I'll see if I can boil the GME down to simple terms. Suppose you have a single mass on a spring. You excite it, it bounces. In the absence of drag/friction, it will bounce "forever". Suppose also have a great big collection of masses arranged in (say) a vast cubic lattice, with all masses separated by springs that hold them for (small oscillations) at or near their equilibrium positions. This isn't a terrible model for a lot of things -- a two level atom and the radiation field, a diatomic molecule sitting next to a solid surface. It's also simple enough to be easily modelled with e.g. matlab, if you know how to do that sort of thing.
If you turn on a (weak) coupling between the one oscillator and the oscillator "bath", what happens? Well, the oscillation of the single oscillator will damp out as it transfers energy into the bath. The bath oscillations will almost certainly not remain in any simple coherent mode (which would require a powerful coincidence in the energy structure) but will be transmitted away from the coupling site to make all of the masses bounce just a little bit -- indeed, the simplest way to describe its probable future state is "thermal equilibrium", where it is in one of the near-infinity of states that have the right total energy and the energy is, on average, shared among all of the atoms and bonds equally.
This is a lovely model for irreversible decay, because it describes what we think really h
Personally, I never doubted that the wavefunction is a "real physical object" (whatever that means classically or quantum mechanically). However, the equations of motion of quantum mechanics are as deterministic as the equally "real" equations of motion of classical mechanics. In fact, claiming that the wavefunction is "real" (as in, has objective physical existence) is the exact opposite of asserting that it is indeterministic. Our knowledge may be limited by many things, but the time evolution of the Universal wavefunction itself -- especially if it is "real" -- is not known or believed to be stochastic. If you disagree, we'll have to have a conversation about entropy and you'll have to quote some textbooks or provide some objective support for your point of view.
Oh, I almost forgot -- you might also read Susskind's "Black Hole Wars" -- in it he talks extensively about the fact that QM conserves information, and illuminates why the issue is so very important, critical to the global consistency of the theory, and how strongly that constrains the physics of black holes (among many other things...:-). Entropy is missing information, and the theme of the entire book is the story of how Hawking's original models for black holes increased the entropy of the universe by letting you drop information irreversibly into one, and how badly that would break quantum mechanics (if true). In the end, it appears that it simply is not true, with profound consequences that are still being explored. Great read, accessible to any reasonably well read physics groupie on up, no real math required.
Not precisely relevant to the GME, except that it establishes the principle that at the cosmological TOE level, QM (to be consistent) is zero (real) entropy, quite different from the APPARENT entropy we assign to a given system based on coarse-grain averaging over the internal degrees of freedom required to precisely specify the microstate. One is a measure of our ignorance of (indestructible) state information; the other is a measure of the actual INFORMATION CONTENT of state and whether or NOT it is creatable or destroyable. The latter is downright metaphysical; the former is (necessary, useful, essential) computational trickery.
Wonderen and Lendi: Journal of Statistical Physics, Vol. 80, Nos. 1/2, 1995
Kapral and Ciccotti: JOURNAL OF CHEMICAL PHYSICS VOLUME 110, NUMBER 18 8 MAY 1999
Sorry about the caps, I'm cutting and pasting from pdfs.
Carmichael and Walls: 976 J. Phys. B: At. Mol. Phys. 9 1199
This latter one is a classic -- you might want to start with it first, because it is the simplest one to understand AND contains the most amazing physics, deriving Hanbury-Brown and Twiss-style second order photon correlation in the GME approach (among many other things). Quantum optics is a place where one could really see, and check, the computational correctness of the approach as one derives experimentally checkable results from APPROXIMATIONS of the actual motion for the complete system, subject to the imposition of a statistical description of the "bath". It also gives you real insight.
Yeah, it does presuppose that you have completed at least 2 semesters of quantum theory if not three and that you are at least as good at math as anybody has to be to have done so, but other than that the BASIC formulation is pretty straightforward, the density matrix formulation of quantum mechanics masssaged a bit. The integrals and so on eventually get pretty hairy, but this is where you LEARN a lot about that sort of thing. The algebra itself is not for the faint of heart -- it is Not Easy (tm) even compared to run of the mill perturbation theory and so on. That's really, ultimately, why it is so rarely taught -- not that many people know it well enough to teach it and there aren't that many books, especially "textbooks", that include it.
That's why I'd advise reading FIRST just the INTRODUCTION -- the part about \rho-dot, splitting \rho, and inventing a P, then wrapping the latter through the former. If you can understand that -- what they are trying to do and why they are doing it -- then you can get the IDEAS behind the GME and why they are so important in understanding both quantum theory itself (without pesky pseudocontradictions in the nonrelativistic semi-classical descriptions used in most intro texts where they hide the partitioning of the quantum system from the classical measurement apparatus from you by talking about it the first day and then NEVER RETURNING TO IT to show that the theory is ultimately consistent without a "classical" object in it) and quantum stat mech, especially the stat mech of open systems.
That's really what it is all about. The correct statistical description of open systems.
Read the Breuer article -- it is super. It still isn't super enough -- you really need to read articles where the GME approach is used (by Agarwal and others) to e.g. derive the Einstein A coefficient for spontaneous emission by coupling a "two level atom" to an infinite mode EM field, and contrast the result with e.g. Rabi oscillations when you couple the SAME atom to a single mode field. The latter oscillates forever, the former exponentially damps as the "irreversible" decay is seen to be the stretching to infinity of a multimodal periodicity (return time for the e.g. oscillator with N \to \infty springs). Loudon has a nice treatment of this in optics, where the GME can actually be formulated and (with suitable renormalization) solved in the Markov approximation.
The sad thing is that very few people understand the philosophical implications of following the Nakajima-Zwanzig path, especially if one attempts to do so in a relativistically invariant framework. Basically, all of the "contradictions" of quantum theory disappear, revealed to be consequences of our ignorance of global state or unreasonable idealizations or both.
My favorite example is Schrodinger's damnable cat inside its infernal device, the sealed safe containing a radioactive sample that triggers poison and supposedly moves the cat from being a pure state of living cat into a quantum entangled superposition of live cat and dead cat. What nonsense! As if you can even disentangle the cat, the radioactive sample, the "sealed" safe, and everything else inside the box from everything on the outside of the box! Ever single elementary particle inside the box is coupled, directly or indirectly, via interactions that you can no more turn off than fly to the moon, to every other elementary particle in the Universe outside of the box. They were "entangled" (if you like) when the cat went into the box, they are still entangled when the cat emerges, and at no point did anything "random" or "magical" happen to all of the phases in the BIG density matrix that describes the entire system. If there were any such rot, we'd all be eternally in just such a split state of dead and not dead, because at every instant there are countless pathways that lead from instant to instant including some in which we die.
Or, perhaps this explains why there are so many zombies in the world today, their wavefunctions gradually becoming a weighted mix of mostly-dead... I have no idea;-)
Of course, a really good physics lecturer would have pointed out that the entropy of a closed system is constant. He or she might then go on to point out that -- in both classical and quantum mechanics -- the time evolution from any given initial condition is completely deterministic. Since entropy is the natural log of the missing information, and in a closed physical system that evolves in time according the solution to what amounts to a four-dimensional boundary value problem there is no missing information, not only is the entropy constant the entropy is zero.
A really great physics lecturer would then go on to point out that if one takes said closed Universe and partitions it (mentally) into a (sub) "system" and its complement (everything else), the "bath", defines Nakajima-Zwanzig projection valued operators and performs a ritual incantation involving several pages of very difficult algebra and calculus, one arrives at a set of non-Markovian integrodifferential equations that describe the still-deterministic time evolution of the subsystem in contact with the bath, from the full set of initial conditions of the whole thing (including all phases in quantum theory). This lecturer could then talk about making Markov approximations to get rid of the integro- part of the solution, about the impossibility of our obtaining sufficiently complete knowledge of the bath and hence the necessity of diagonalizing it (taking the trace in QM) and thereby describing it classically and statistically, and perhaps even discuss the Langevin equation as a solvable stochastic ODE that can model the system in contact with the bath and THEN note that under these conditions, the "entropy" of the system must increase as its initial information diffuses into the basically unknown state of the bath.
He/she might title the lecture "The Generalized Master Equation and open systems in quantum mechanics", and stick it in close to the end of a good stat mech course, and perhaps direct the reader to some of the lovely review literature, e.g. an article by Breuer at arXiv:0707.0172v1.
Sadly, even in most physics departments there are still far too many faculty who are teaching what they were taught by rote -- that quantum mechanics is somehow "fundamentally non-deterministic". Not so, as the equations of motion of quantum theory themselves quite clearly demonstrate (being well-defined systems of differential equations for any closed system). It's only when one considers measurement that stochastic descriptions come into play, and the consistently derived reason is precisely that outlined above. We cannot describe the measurement apparatus itself as part of the quantum system with a definitely known state so we treat it classically and statistically via e.g. traces and random phase approximations and the like (or just treat it as a classical stochastic filter).
I agree! Praise the Holy Loaded Dice of Ifni, that manage to make everything that happens look like there is a truly enormous amount of entropy and both governed by and described by the enormously successful theory of statistical mechanics and its underlying Bayes theorem! How clever of her! Or, of course, the Dice could really be random, and She could roll entire space-time continua the way we idly flip coins or randomly initiate Conway's Game of Life just to see if anything "interesting" pops out.
Hey, at least it passes eternity...
It does leave one with many important questions to answer. What is the relationship between Ifni and the FSM? Is J. "Bob" Dobbs their Holy Offspring? How do pirates apparently regulate global temperatures? Does Ifni script her Universes by using actual monkeys at typewriters? Where does she get the monkeys, and for that matter, the typewriters?
One can hardly blame the Muslims for walking out. It is obvious that anything that appears to be perfectly random and governed by impersonal microdynamic forces really isn't. Any fool could see that there must be a far, far more complex system in existence somewhere else that created all of this apparent randomness and that precomputes all of the time evolution of those microdynamic forces in a system that spans at least 200 billion LY (limit established by inferences based on observed homogeneities and certain assumptions of continuity) that is so large that its various parts aren't even causally connected post-Big Bang.
I'm not completely convinced of this, because the state of the atoms in the surrounding space will be strongly perturbed by the time-varying induced voltages, not just the static coulomb voltage. I would be very surprised if the "lightning" coming off of tesla coils is structured like real lightning precisely at the avalanche for this reason. The initiation of dielectric breakdown in a gradually building radial static field seems as though it would be very different from dielectric breakdown through atoms that have more or less been kicked in the ass sideways by an EMP. Tesla coils RADIATE a large amount of transverse energy throughout their time-dependent cycle, and this energy clearly alters the velocity distribution of nearby atoms to nonthermal "instantly" (nonthermal in the specific sense that they aren't even locally describable by a "temperature") and if they were (averaging) they would be "hot", preheated by eddy currents BEFORE the peak voltage and discharge occur. DC charged clouds OTOH one would expect would heat the surrounding air BY the incipient dielectric discharge, quite possibly over a timescale of seconds as the voltages gradually build and increase the electrostatic wind (nearby air atoms that pick up charge and are strongly repelled, banging through neutral atoms being weakly attracted the other way by straight-up induced dipole forces). In this case one would expect at least sufficient time for local equilibrium to be achieved, enough so that one could speak of the nucleation and growth of the distribution of higher temperatures in the surrounding air, maybe?
So, I'm curious -- given that you are going to be spending big science money on two 200 foot tesla coils (why two? Why not one and a large conducting sheet so that it sees its own mirror if it is really "DC" enough to ignore eddy currents?) why not build a single giant vandegraff, one with a primary ball made out of e.g. a 10+ meter radius mylar balloon floated over a very large conducting floor so that it sees its own image charge instead of a second, equally expensive primary?
Rule of thumb 30kV * R(cm) = V_discharge suggests that a 10 meter radius sphere should arc at 30 MV in air, and it should also have a very large capacitance (so that the energy in an arc discharge should be quite large). An inflated mylar sphere should be cheap enough to be a consumable item, if it comes to that, and the lightning produced by such a device would be very close to REAL lightning in its form and structure because the mylar sphere is actually a model for a real cloud. Indeed, one could use blimp-shaped or irregularly shaped objects to further model the irregular shapes of clouds that increase the capacitance while decreasing the peak breakdown voltage.
Not that I don't appreciate the desire to create really big sparks, mind you, and tesla coils do make much more impressive ongoing displays... I would just argue that it is reasonable to doubt that the answers you get from a tesla coil would necessarily apply to real lightning where the answers one would get from a supersized vandegraff -- even though they are still on a smaller scale than real clouds -- are much more likely to be scalable and to exhibit the right features at all scales. And if you buy a used goodyear blimp and cover it with e.g. aluminum vapor and use it as the primary tethered to the top of a 100 meter tower, you would be pretty close to the actual scale of a cloud...
Sure, I guess, but personally I don't know of many physicists who believe, or teach, that the Copenhagen interpretation is correct and everybody is dubious of the many worlds hypothesis because a) there is no obvious way to test it; and b) it causes an explosion of nature to cover not just Leibnitz' (or Dr. Pangloss') "best of all possible worlds" but all possible worlds. One might as well believe in magic as this is a religious assertion until it is demonstrated that there is an experimental observation that not only "can" be explained by many worlds, but REQUIRES many worlds to explain it and of course mathematically that is not only not true it is hardly possible within the confines of quantum theory as we use it computationally.
Besides, it isn't necessary. As noted, measurement is essentially a classical process and most of the "paradoxes" in any theory of quantum mechanics come from e.g. inappropriately separation and diagonalization of the Universe into system and everything else. The simplest explanation that agrees with the observations has ALWAYS been that the wavefunction of an electron is as real as the electron itself, although the idea of a "single electron wavefunction" is a bit of a myth, an idealization that we can basically never realize. Insisting that it be unreal clearly is an a priori assertion without any foundation. Insisting that it is real in an infinite hypervolume of entire spacetime continua with combinatorial/permutative complexity is is an a priori assertion with infinitely less foundation. Assigning it the provisional value of being real unless or until proven otherwise has been the default ever since it was shown that electrons exhibit two slit interference and all other wave phenomena in the appropriate context, since Aharonov-Bohm, since the electron microscope, really since de Broglie.
With that said, I'm quite glad to see that there is MORE evidence confirming my longstanding beliefs -- I'd just assert that it is just more, not the first or only.
Again, wrong perspective. Particles never "become" entangled. This is a local view that directly contradicts relativistic quantum field theory and is inconsistent. Particles -- and I mean every particle in the universe, at least indirectly, if one views it as a manifold -- are always entangled. There is just one "Universal" wavefunction, and it either must be stationary (closed Universe) or it else we have to work very hard to understand information conservation as we observe it in the part of the Universe we can see. The only approach, either way, is to follow the general derivation of the Generalized Master Equation, the partition of a presumed stationary universal wavefunction into a "system" and a "bath". The system is treated as an internally deterministic time evolution, but the bath is treated statistically not because it isn't really quantum mechanical, but because we cannot know its initial state any better than probablistically, we cannot prepare it in a known pure state, its state is known classically. Hence a diagonal trace and the introduction of projection valued operators. This is where Bell's theorem appears, and where the whole dogma of the measurement of quantum SUBsystems appears, where an effective random phase approximation appears, where quantum indeterminacy in the subsystem appears. It's all smoke and mirrors -- it doesn't exist in the proper original statement of the problem, it only appears at a certain point where we make necessary approximations due to our IGNORANCE of the state of the bath.
It's all about information.
Describe to me the "time evolution of entanglement" otherwise. You can't. "Entanglement" occurs only when you mentally prepare the system initially in a product state, and then allow time evolution to carry you into a matrix representation. But this is a false dilemma -- the system was NEVER really in a product state -- it was at best in a diagonal state in the matrix representation in the first place, and ANY interaction with the outside world suffices to move you out of it. That interaction with the outside world cannot ever be turned off, right? It is merely -- incorrectly -- ignored. Hence Schrodinger's Cat is a quantum paradox only if you presume COMPLETE ADIABATIC DECOUPLING of the box and infernal device from the rest of the Universe, which is of course absurd.
An interesting hypothesis indeed, although I remain a wee bit skeptical. But a good provisional explanation, no doubt. Leonard writes very convincingly...;-)
That's the point, if one is inclined to examine the metaphysical philosophy underlying quantum mechanics or any other mental map of a supposed external reality. The questions involved are very old, and the only reasonable path from Humian skepticism to knowledge as a network of reasonably consistent probable truth is that laid out originally by Richard Cox, then emphatically recapitulated by E. T. Jaynes. A great deal of bootstrapping occurs as we seek the optimum solution to this problem -- as in belief in our neural states and visual cortex comes from analyzing sensory impressions that, it appears, occur in our neural apparatus and visual cortex, both objects and means consistently. However, both the "evil genius"/Matrix and the solipsistic solutions exist as an eternal counterexample against assertions that we can be certain of what external reality REALLY is.
Given that, there has never been any good reason (post 1930s) to doubt the "reality" (objective existence) of a wavefunction, any more than there is good reason to doubt the reality of the electron in a wavefunction or the atom made out of the electrons and so on. By this I don't mean that we can't and don't continue to doubt -- I mean that in the near infinity of possible notional "alternative explanations" for all of the experiments and observations we make about "reality", the simplest solution that best fits the facts has long, long been that wavefunctions are as real as anything else -- they are a provisional truth in excellent agreement with experiment and consistently connected with an entire system that works pretty well.
Can we be certain that it is correct? Of course not. But no reasonable person has been able to doubt their reality more than the alternative explanations, as the alternative explanations have little explanatory power and or usually openly inconsistent in one place or another. Most of the objections are predicated upon our essentially classical everyday experience and the fact that our brains are evolved to optimally "think" classically, but it has long been known that quantum mechanics is as logically/mathematically consistent as classical mechanics -- indeed, if you read Schwinger's lovely "Quantum Kinematics and Dynamics" you can see the precise point where the worldview diverge, from the purely common sense description of measurement processes as an abstract algebra.
Bell's theorem's implication is that their are not "hidden variable" theories that can explain quantum mechanics.
Wrong. Bell's theorem's implication is that there are no local hidden variable theories which can explain quantum mechanics. Non-local hidden variable theories are not excluded by Bell.
I'd even go one further -- it isn't clear what Bell's theorem implies as soon as you make quantum mechanics properly relativistic and time reversible within a closed physical universe, so that the measurement process it relies on no longer involves entropy in the form of an uncontrolled interaction with a classical measuring apparatus in an unknown microstate. In other words, Bell's theorem is completely meaningless as far as the nature of the actual state or nature of the Universe is concerned; it at best describes a theory of time-ordered, entropy based, projective measurements on open quantum subsystems.
As far as that is concerned, how could one NOT interpret the wavefunction as being "real" (given that a rather lot of it is imaginary if not quaternionic or a number in a generalized geometric division algebra of higher grade:-). It's no more real or less real than any model of a postulated external reality based on our sensory impressions and data, reinforced by reason-based statistical inference.
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(Yeah, yeah, I get it, they are really just trying to say that "time-ordered phenomena apparently exist so the wavefunction must be real", but why bother?. Did any physicist for the last sixty years or so ever doubt this? Should they have, any more than they doubt that reality itself is real and we aren't really all power units in The Matrix?)
Well, yes, I did think about that possibility as well, especially robots with certain useful, ummm, "attachments". Or features. Or whatever. But really, ho-bots are not news; they have been readily available for decades at least with every bit as much intelligence as the real thing.
Well, perhaps $1000 per row -- as I noted at the end, it might be better to build a large hoebot capable of doing 20 rows at once with a single brain. The issue of batteries vs solar (or some mix of the two) would have to be worked out on a cost-benefit basis. Assuming 20 rows 1 meter wide (each), one could cover the entire unit with 10KW worth of cells fairly simply, which gives you more than enough energy to move forward at a steady crawl and perform both the computational and cultivational tasks. That's half the budget of a $20K machine. You're right, even $1000/row might be an underestimate, but it's all capital investment with a potentially long amortization and substantial cost savings (no need to buy expensive chemicals and expensive machinery to safely dispense those chemicals). Those aren't cheap either, and they are an annual expense that leaves you at the mercy of the big agrichemical companies and the manufacturers of farm equipment and various inspectors and the risk that one day somebody will discover that the insecticide you are using causes birth defects or the like and force you completely alter your farming methodology and repurchase capital equipment and shift to yet another chemical (that is without doubt going to be more expensive). Also, mass production should improve economy of scale.
I really don't think it will cost $200K for a production hoebot capable of doing 20 row swatches at a rate of a few meters a minute -- that's more what I would expect to spend building a prototype by hand out of over the counter materials. $10-20K for solar cells and battery backup. Some hefty electric motors for primary motion. Over the counter "robot arms" with a small rotary cultivator on the end and a cheap USB CCD binocular camera. A simple, lightweight PVC "trestle" to connect the brain to the per-row wheels and cultivator units, provide channels for the control wiring, and support the solar array. I actually think it would be pretty bone simple to build a prototype for a hardware budget of $250K (plus whatever sweat-equity in a startup is worth for labor, testing, and coding). I could be wrong, though.
With a prototype in hand, it would then be straightforward to redesign it to be cheap and mass-producible, which ought to cut costs by quite a bit...
The article misses the long term point. One day a small team of farmbots can and will replace both herbicide and insecticide and, to some extent, fertilizer. Powered by the sun, they will spend all daylight hours simply moving up and down the rows of desired plants, distinguishing them from non-desired plants by AI, and using very simple tools to remove/kill those plants. They will similarly be able to identify and kill or spot treat various undesireable "bugs" and other parasites or diseases. They will be able to do things such as loosen the soil above the root masses of the plants to permit optimal penetration of water, precisely mulch and/or fertilize each plant, replant seedlings as they die in the early going so that the field is optimally productive, and quite possibly will be able to deliver just enough water to plants to keep them healthy during at least moderate droughts.
A farmbot capable of all of these things, powered by solar cells, shouldn't cost more than $1000 in a production (not research) environment. The computer guts for it are all cheap by now. It's little more than a Roomba repurposed to "vacuum" down the rows of a field (and hardened against the elements). The hard part is just writing the software, and that's all one time capital investment. A single month's worth of work from one would likely pay for it in reduced labor and chemical costs, not to mention the price premium for "organic" food as more and more people recognize that dumping chlorinated hydrocarbons and neurotoxins onto our food year after year is probably not a really stellar idea.
This may not happen this year, or even this decade, but I think that it is very likely to be coming. Perhaps this startup won't make it. Perhaps it will, using modest success with this very humble precursor to fund gradual improvements until they achieve it. But humans haven't the patience to do the kind of work that a farmbot will do, not at any price, neither domesticated nor imported. Tireless, working from sunup to sundown, processing order of meters of row per minute it will be able to keep one or more acre of planted crop "perfectly" productive without the use of chemicals or far more expensive human time.
Oh, it may not be configured LIKE a roomba as a single crawler -- it may be more effective to build it as (for example) a single brain in a larger, more expensive chassis that can process ten or twenty rows at a time (plenty of cycles to accomplish this in a single central computer, especially with multiple cores). But it's coming.
Slashdot Mirror
Let me try to put this in context for you:
I sure as hell don't know what is really going on with all of that.
There, is that better? No, I'm not a neutrino expert, and I certainly haven't spent a lot of time studying tachyons, given that up until now there hasn't been any real experimental evidence that they exist (and the jury is still out on whether the current evidence is "real"). I was just kidding around with the neutrinos, as well because I am no neutrino expert. When I went to grad school neutrinos were believed to (maybe) be massless! As for trusting me about the GME -- who asked you to? Read the papers!
In the meantime, yeah, if the neutrino result pans out I suspect that I won't be the only person going back to learn or refresh memory of the consequences of that great range of trajectories outside of the light cone. In my case, one of the puzzles will be trying to reconcile the result with a presentation I attended back in the 80's (at a lunch seminar in our theory group) where a very reputable physicist argued that there must be a upper bound speed that is the same for everything, not just light, on grounds that were somewhat different from the usual relativity arguments. Unfortunately, I have no memory of whether or not it was ever published, and obviously don't remember enough to know if it was persuasive or correct. But I do think that it is safe to say that it will have some fairly profound consequences in LOTS of places...
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Piffle. This is the sort of nonsense that makes people thing quantum theory is crazy or, worse, inconsistent. The very sentence is you use to state this is self-contradictory and hence meaningless. If one has perfect knowledge of the wavefunction and its time evolution, then one cannot "only probabilistically describe its behavior".
What you mean to say -- I suspect -- is that the outcome of certain measurements performed on a quantum system that is initially prepared in a specific state is only predictable probablistically (where other measurements might be completely predictable). What you are neglecting is that the measuring apparatus in this case is a) not considered part of the quantum system; b) is in an unknown initial quantum state; c) is in an initial quantum state that is essentially (semi)classical, in particular is considered to be prepared independent of the system state so that the two are in an outer product (non-entangled) state as part of your initial conditions.
The correct quantum description of the full problem would a) make the measuring apparatus a part of the quantum system; b) require the whole quantum system to be in a known initial state; c) that almost certainly would not be non-entangled, if you consider time reversal invariance. In this full problem there is no indeterminacy and no probability, only time evolution of a fully specified system wavefunction.
Probability enters quantum theory only at the point of measurement, and there it is a measure of our ignorance of state, not a measure of some intrinsic entropy content in a closed quantum system.
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No, I don't understand either. I just pretend to -- not a troll, just an acknowledgement that 30 years after I got MY Ph.D. (next year) and in spite of teaching quantum and publishing papers in quantum and CMP, -- I think of most physics as "something I should understand, but don't". Some things I do pretty well on. Other things, my knowledge is positively embarrassing, or would be, if I cared.
FWIW, it took me an easy decade of post-Ph.D. existence AND those many papers before I started to get semi-comfortable with quantum theory, and even now my knowledge is very subject to fluctuation, forgetfulness, and fog -- a lot more fog as I get older. Some things get clearer and make more sense, but others become even more obscure.
The amazing thing is that if you dedicate yourself to any particular problem in QM or QFT, you often CAN make a real contribution. Sometimes it takes a decade or two. Sometimes the real contribution is a very MODEST real contribution. But every now and then somebody turns out to be a Feynman, often surprising even themselves...;-)
So don't give up.
See other replies -- one has a few references. As for entropy, that's tough. Probably E.T. Jaynes, but other than Probability Theory, the Logic of Science I don't have a good reference at my fingertips. You could try googling "information theoretic approach to statistical mechanics" and see what turns up -- the entropy as the log of the missing information arises in this approach, which in turn arises from Jaynes and the work of Richard Cox first, Claude Shannon second. It's probably in various stat mech textbooks at this point -- but I was lucky enough to take stat mech from Richard Palmer, and he taught information theory as the sound(est) axiomatic basis for stat mech from the beginning, and much older and wiser now -- I still think he was dead right.
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Ah, but this means that there IS no eventual heat death of the Universe. Well, it would mean that if it weren't for the open vs closed issue. Doesn't really restrict what happens to an open Universe much...:-)
...by hacking into the corporate network of the company you want to work for and obtaining compromising material, such as uploaded video porn involving the company president and a local group of cheerleaders (female and male cheerleaders work best), the numbers of the offshore accounts of major corporate officers -- don't be tempted or distracted by this, by the way, we're trying to get a job, not get rich directly, that sort of thing. You might want to encrypt their entire customer database as well with a key Only You Know. After this, a subtle hint in the right place -- one that just appears in their mailbox as if by magic -- should do the trick, without needing to resort to similar email messages in the mailboxes of their wives, husbands, federal agents working for the IRS, BATF, DEA and FBI. One hopes.
What, you disagree? Strange, it has always worked for me...;-)
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P.S. -- and if it doesn't, well, there are always all of those account numbers...
It's no joke. Read the papers. Although if most people knowing what the hell REALLY goes on in quantum theory is a criterion for science not being in trouble, well, it's been in serious trouble for over a century now. As Feynman said, "Nobody understands Quantum Mechanics."
/. The only way I can pay it forward is to try to post informative stuff on the little patches I've studied pretty deeply and mostly understand. I'm hell on wheels for certain kinds of Green's functions in the context of integral equation solutions to PDEs in quantum or classical field theories, not bad on quantum optics or critical phenomena or certain aspects of quantum stat mech (and generally competent in basic quantum mechanics, enough to teach it). I'm terrible wrt other stuff in physics -- it is too big, and too difficult to master it all.
QM and GR (and their synthesis, fully relativistic quantum field theory) are just a bit too difficult for the human brain to fully grasp. Every decade or two a human comes along who by serendipitous chance and hard work is Einstein, Lobachevsky, Riemann, Dirac, Ramanujan, Gauss, Feynman brilliant and things advance a bit, often quite abruptly. Then we are once again stuck as we labor to overcome the flaws in what we've figured out, which sometimes require complete paradigm-shifting rearrangements of what we know. At the same time all of this is going on, new experimental evidence is constantly being produced, some of which might well reveal truly new physics, not just more about what we already know, or think we know.
We live in interesting times. Dark matter, dark energy have burst on the scene. Neutrinos have a mass. Neutrinos might go faster than the speed of light (negative mass?). The LHC has failed to find the Higgs -- again -- in a great deal of the range which -- again -- it was claimed that it would/might/should be found. Magnetic monopoles are rarely found, but never reproducibly, and hover around on the boundary of believability. Gravity remains a cruel puzzle, a deep inconsistency between quantum theory and general relativity. We still have no direct evidence concerning whether antiparticles are gravitationally attracted to particles or repelled by them! Hell, if neutrinos do have negative mass, and negative mass gravitationally repels ordinary mass, then the neutrino content of a galaxy is conceivably the missing "dark matter".
I sure as hell don't know what is really going on with all of that. One of many reasons I read
I'll see if I can boil the GME down to simple terms. Suppose you have a single mass on a spring. You excite it, it bounces. In the absence of drag/friction, it will bounce "forever". Suppose also have a great big collection of masses arranged in (say) a vast cubic lattice, with all masses separated by springs that hold them for (small oscillations) at or near their equilibrium positions. This isn't a terrible model for a lot of things -- a two level atom and the radiation field, a diatomic molecule sitting next to a solid surface. It's also simple enough to be easily modelled with e.g. matlab, if you know how to do that sort of thing.
If you turn on a (weak) coupling between the one oscillator and the oscillator "bath", what happens? Well, the oscillation of the single oscillator will damp out as it transfers energy into the bath. The bath oscillations will almost certainly not remain in any simple coherent mode (which would require a powerful coincidence in the energy structure) but will be transmitted away from the coupling site to make all of the masses bounce just a little bit -- indeed, the simplest way to describe its probable future state is "thermal equilibrium", where it is in one of the near-infinity of states that have the right total energy and the energy is, on average, shared among all of the atoms and bonds equally.
This is a lovely model for irreversible decay, because it describes what we think really h
Personally, I never doubted that the wavefunction is a "real physical object" (whatever that means classically or quantum mechanically). However, the equations of motion of quantum mechanics are as deterministic as the equally "real" equations of motion of classical mechanics. In fact, claiming that the wavefunction is "real" (as in, has objective physical existence) is the exact opposite of asserting that it is indeterministic. Our knowledge may be limited by many things, but the time evolution of the Universal wavefunction itself -- especially if it is "real" -- is not known or believed to be stochastic. If you disagree, we'll have to have a conversation about entropy and you'll have to quote some textbooks or provide some objective support for your point of view.
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Oh, I almost forgot -- you might also read Susskind's "Black Hole Wars" -- in it he talks extensively about the fact that QM conserves information, and illuminates why the issue is so very important, critical to the global consistency of the theory, and how strongly that constrains the physics of black holes (among many other things...:-). Entropy is missing information, and the theme of the entire book is the story of how Hawking's original models for black holes increased the entropy of the universe by letting you drop information irreversibly into one, and how badly that would break quantum mechanics (if true). In the end, it appears that it simply is not true, with profound consequences that are still being explored. Great read, accessible to any reasonably well read physics groupie on up, no real math required.
Not precisely relevant to the GME, except that it establishes the principle that at the cosmological TOE level, QM (to be consistent) is zero (real) entropy, quite different from the APPARENT entropy we assign to a given system based on coarse-grain averaging over the internal degrees of freedom required to precisely specify the microstate. One is a measure of our ignorance of (indestructible) state information; the other is a measure of the actual INFORMATION CONTENT of state and whether or NOT it is creatable or destroyable. The latter is downright metaphysical; the former is (necessary, useful, essential) computational trickery.
Breuer's article (xref'd above, or google it up).
Wonderen and Lendi: Journal of Statistical Physics, Vol. 80, Nos. 1/2, 1995
Kapral and Ciccotti: JOURNAL OF CHEMICAL PHYSICS VOLUME 110, NUMBER 18 8 MAY 1999
Sorry about the caps, I'm cutting and pasting from pdfs.
Carmichael and Walls: 976 J. Phys. B: At. Mol. Phys. 9 1199
This latter one is a classic -- you might want to start with it first, because it is the simplest one to understand AND contains the most amazing physics, deriving Hanbury-Brown and Twiss-style second order photon correlation in the GME approach (among many other things). Quantum optics is a place where one could really see, and check, the computational correctness of the approach as one derives experimentally checkable results from APPROXIMATIONS of the actual motion for the complete system, subject to the imposition of a statistical description of the "bath". It also gives you real insight.
Yeah, it does presuppose that you have completed at least 2 semesters of quantum theory if not three and that you are at least as good at math as anybody has to be to have done so, but other than that the BASIC formulation is pretty straightforward, the density matrix formulation of quantum mechanics masssaged a bit. The integrals and so on eventually get pretty hairy, but this is where you LEARN a lot about that sort of thing. The algebra itself is not for the faint of heart -- it is Not Easy (tm) even compared to run of the mill perturbation theory and so on. That's really, ultimately, why it is so rarely taught -- not that many people know it well enough to teach it and there aren't that many books, especially "textbooks", that include it.
That's why I'd advise reading FIRST just the INTRODUCTION -- the part about \rho-dot, splitting \rho, and inventing a P, then wrapping the latter through the former. If you can understand that -- what they are trying to do and why they are doing it -- then you can get the IDEAS behind the GME and why they are so important in understanding both quantum theory itself (without pesky pseudocontradictions in the nonrelativistic semi-classical descriptions used in most intro texts where they hide the partitioning of the quantum system from the classical measurement apparatus from you by talking about it the first day and then NEVER RETURNING TO IT to show that the theory is ultimately consistent without a "classical" object in it) and quantum stat mech, especially the stat mech of open systems.
That's really what it is all about. The correct statistical description of open systems.
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Read the Breuer article -- it is super. It still isn't super enough -- you really need to read articles where the GME approach is used (by Agarwal and others) to e.g. derive the Einstein A coefficient for spontaneous emission by coupling a "two level atom" to an infinite mode EM field, and contrast the result with e.g. Rabi oscillations when you couple the SAME atom to a single mode field. The latter oscillates forever, the former exponentially damps as the "irreversible" decay is seen to be the stretching to infinity of a multimodal periodicity (return time for the e.g. oscillator with N \to \infty springs). Loudon has a nice treatment of this in optics, where the GME can actually be formulated and (with suitable renormalization) solved in the Markov approximation.
The sad thing is that very few people understand the philosophical implications of following the Nakajima-Zwanzig path, especially if one attempts to do so in a relativistically invariant framework. Basically, all of the "contradictions" of quantum theory disappear, revealed to be consequences of our ignorance of global state or unreasonable idealizations or both.
My favorite example is Schrodinger's damnable cat inside its infernal device, the sealed safe containing a radioactive sample that triggers poison and supposedly moves the cat from being a pure state of living cat into a quantum entangled superposition of live cat and dead cat. What nonsense! As if you can even disentangle the cat, the radioactive sample, the "sealed" safe, and everything else inside the box from everything on the outside of the box! Ever single elementary particle inside the box is coupled, directly or indirectly, via interactions that you can no more turn off than fly to the moon, to every other elementary particle in the Universe outside of the box. They were "entangled" (if you like) when the cat went into the box, they are still entangled when the cat emerges, and at no point did anything "random" or "magical" happen to all of the phases in the BIG density matrix that describes the entire system. If there were any such rot, we'd all be eternally in just such a split state of dead and not dead, because at every instant there are countless pathways that lead from instant to instant including some in which we die.
Or, perhaps this explains why there are so many zombies in the world today, their wavefunctions gradually becoming a weighted mix of mostly-dead... I have no idea;-)
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Of course, a really good physics lecturer would have pointed out that the entropy of a closed system is constant. He or she might then go on to point out that -- in both classical and quantum mechanics -- the time evolution from any given initial condition is completely deterministic. Since entropy is the natural log of the missing information, and in a closed physical system that evolves in time according the solution to what amounts to a four-dimensional boundary value problem there is no missing information, not only is the entropy constant the entropy is zero.
A really great physics lecturer would then go on to point out that if one takes said closed Universe and partitions it (mentally) into a (sub) "system" and its complement (everything else), the "bath", defines Nakajima-Zwanzig projection valued operators and performs a ritual incantation involving several pages of very difficult algebra and calculus, one arrives at a set of non-Markovian integrodifferential equations that describe the still-deterministic time evolution of the subsystem in contact with the bath, from the full set of initial conditions of the whole thing (including all phases in quantum theory). This lecturer could then talk about making Markov approximations to get rid of the integro- part of the solution, about the impossibility of our obtaining sufficiently complete knowledge of the bath and hence the necessity of diagonalizing it (taking the trace in QM) and thereby describing it classically and statistically, and perhaps even discuss the Langevin equation as a solvable stochastic ODE that can model the system in contact with the bath and THEN note that under these conditions, the "entropy" of the system must increase as its initial information diffuses into the basically unknown state of the bath.
He/she might title the lecture "The Generalized Master Equation and open systems in quantum mechanics", and stick it in close to the end of a good stat mech course, and perhaps direct the reader to some of the lovely review literature, e.g. an article by Breuer at arXiv:0707.0172v1.
Sadly, even in most physics departments there are still far too many faculty who are teaching what they were taught by rote -- that quantum mechanics is somehow "fundamentally non-deterministic". Not so, as the equations of motion of quantum theory themselves quite clearly demonstrate (being well-defined systems of differential equations for any closed system). It's only when one considers measurement that stochastic descriptions come into play, and the consistently derived reason is precisely that outlined above. We cannot describe the measurement apparatus itself as part of the quantum system with a definitely known state so we treat it classically and statistically via e.g. traces and random phase approximations and the like (or just treat it as a classical stochastic filter).
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I agree! Praise the Holy Loaded Dice of Ifni, that manage to make everything that happens look like there is a truly enormous amount of entropy and both governed by and described by the enormously successful theory of statistical mechanics and its underlying Bayes theorem! How clever of her! Or, of course, the Dice could really be random, and She could roll entire space-time continua the way we idly flip coins or randomly initiate Conway's Game of Life just to see if anything "interesting" pops out.
Hey, at least it passes eternity...
It does leave one with many important questions to answer. What is the relationship between Ifni and the FSM? Is J. "Bob" Dobbs their Holy Offspring? How do pirates apparently regulate global temperatures? Does Ifni script her Universes by using actual monkeys at typewriters? Where does she get the monkeys, and for that matter, the typewriters?
One can hardly blame the Muslims for walking out. It is obvious that anything that appears to be perfectly random and governed by impersonal microdynamic forces really isn't. Any fool could see that there must be a far, far more complex system in existence somewhere else that created all of this apparent randomness and that precomputes all of the time evolution of those microdynamic forces in a system that spans at least 200 billion LY (limit established by inferences based on observed homogeneities and certain assumptions of continuity) that is so large that its various parts aren't even causally connected post-Big Bang.
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I'm not completely convinced of this, because the state of the atoms in the surrounding space will be strongly perturbed by the time-varying induced voltages, not just the static coulomb voltage. I would be very surprised if the "lightning" coming off of tesla coils is structured like real lightning precisely at the avalanche for this reason. The initiation of dielectric breakdown in a gradually building radial static field seems as though it would be very different from dielectric breakdown through atoms that have more or less been kicked in the ass sideways by an EMP. Tesla coils RADIATE a large amount of transverse energy throughout their time-dependent cycle, and this energy clearly alters the velocity distribution of nearby atoms to nonthermal "instantly" (nonthermal in the specific sense that they aren't even locally describable by a "temperature") and if they were (averaging) they would be "hot", preheated by eddy currents BEFORE the peak voltage and discharge occur. DC charged clouds OTOH one would expect would heat the surrounding air BY the incipient dielectric discharge, quite possibly over a timescale of seconds as the voltages gradually build and increase the electrostatic wind (nearby air atoms that pick up charge and are strongly repelled, banging through neutral atoms being weakly attracted the other way by straight-up induced dipole forces). In this case one would expect at least sufficient time for local equilibrium to be achieved, enough so that one could speak of the nucleation and growth of the distribution of higher temperatures in the surrounding air, maybe?
So, I'm curious -- given that you are going to be spending big science money on two 200 foot tesla coils (why two? Why not one and a large conducting sheet so that it sees its own mirror if it is really "DC" enough to ignore eddy currents?) why not build a single giant vandegraff, one with a primary ball made out of e.g. a 10+ meter radius mylar balloon floated over a very large conducting floor so that it sees its own image charge instead of a second, equally expensive primary? Rule of thumb 30kV * R(cm) = V_discharge suggests that a 10 meter radius sphere should arc at 30 MV in air, and it should also have a very large capacitance (so that the energy in an arc discharge should be quite large). An inflated mylar sphere should be cheap enough to be a consumable item, if it comes to that, and the lightning produced by such a device would be very close to REAL lightning in its form and structure because the mylar sphere is actually a model for a real cloud. Indeed, one could use blimp-shaped or irregularly shaped objects to further model the irregular shapes of clouds that increase the capacitance while decreasing the peak breakdown voltage.
Not that I don't appreciate the desire to create really big sparks, mind you, and tesla coils do make much more impressive ongoing displays... I would just argue that it is reasonable to doubt that the answers you get from a tesla coil would necessarily apply to real lightning where the answers one would get from a supersized vandegraff -- even though they are still on a smaller scale than real clouds -- are much more likely to be scalable and to exhibit the right features at all scales. And if you buy a used goodyear blimp and cover it with e.g. aluminum vapor and use it as the primary tethered to the top of a 100 meter tower, you would be pretty close to the actual scale of a cloud...
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Sure, I guess, but personally I don't know of many physicists who believe, or teach, that the Copenhagen interpretation is correct and everybody is dubious of the many worlds hypothesis because a) there is no obvious way to test it; and b) it causes an explosion of nature to cover not just Leibnitz' (or Dr. Pangloss') "best of all possible worlds" but all possible worlds. One might as well believe in magic as this is a religious assertion until it is demonstrated that there is an experimental observation that not only "can" be explained by many worlds, but REQUIRES many worlds to explain it and of course mathematically that is not only not true it is hardly possible within the confines of quantum theory as we use it computationally.
Besides, it isn't necessary. As noted, measurement is essentially a classical process and most of the "paradoxes" in any theory of quantum mechanics come from e.g. inappropriately separation and diagonalization of the Universe into system and everything else. The simplest explanation that agrees with the observations has ALWAYS been that the wavefunction of an electron is as real as the electron itself, although the idea of a "single electron wavefunction" is a bit of a myth, an idealization that we can basically never realize. Insisting that it be unreal clearly is an a priori assertion without any foundation. Insisting that it is real in an infinite hypervolume of entire spacetime continua with combinatorial/permutative complexity is is an a priori assertion with infinitely less foundation. Assigning it the provisional value of being real unless or until proven otherwise has been the default ever since it was shown that electrons exhibit two slit interference and all other wave phenomena in the appropriate context, since Aharonov-Bohm, since the electron microscope, really since de Broglie.
With that said, I'm quite glad to see that there is MORE evidence confirming my longstanding beliefs -- I'd just assert that it is just more, not the first or only.
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Again, wrong perspective. Particles never "become" entangled. This is a local view that directly contradicts relativistic quantum field theory and is inconsistent. Particles -- and I mean every particle in the universe, at least indirectly, if one views it as a manifold -- are always entangled. There is just one "Universal" wavefunction, and it either must be stationary (closed Universe) or it else we have to work very hard to understand information conservation as we observe it in the part of the Universe we can see. The only approach, either way, is to follow the general derivation of the Generalized Master Equation, the partition of a presumed stationary universal wavefunction into a "system" and a "bath". The system is treated as an internally deterministic time evolution, but the bath is treated statistically not because it isn't really quantum mechanical, but because we cannot know its initial state any better than probablistically, we cannot prepare it in a known pure state, its state is known classically. Hence a diagonal trace and the introduction of projection valued operators. This is where Bell's theorem appears, and where the whole dogma of the measurement of quantum SUBsystems appears, where an effective random phase approximation appears, where quantum indeterminacy in the subsystem appears. It's all smoke and mirrors -- it doesn't exist in the proper original statement of the problem, it only appears at a certain point where we make necessary approximations due to our IGNORANCE of the state of the bath.
It's all about information.
Describe to me the "time evolution of entanglement" otherwise. You can't. "Entanglement" occurs only when you mentally prepare the system initially in a product state, and then allow time evolution to carry you into a matrix representation. But this is a false dilemma -- the system was NEVER really in a product state -- it was at best in a diagonal state in the matrix representation in the first place, and ANY interaction with the outside world suffices to move you out of it. That interaction with the outside world cannot ever be turned off, right? It is merely -- incorrectly -- ignored. Hence Schrodinger's Cat is a quantum paradox only if you presume COMPLETE ADIABATIC DECOUPLING of the box and infernal device from the rest of the Universe, which is of course absurd.
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An interesting hypothesis indeed, although I remain a wee bit skeptical. But a good provisional explanation, no doubt. Leonard writes very convincingly...;-)
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That's the point, if one is inclined to examine the metaphysical philosophy underlying quantum mechanics or any other mental map of a supposed external reality. The questions involved are very old, and the only reasonable path from Humian skepticism to knowledge as a network of reasonably consistent probable truth is that laid out originally by Richard Cox, then emphatically recapitulated by E. T. Jaynes. A great deal of bootstrapping occurs as we seek the optimum solution to this problem -- as in belief in our neural states and visual cortex comes from analyzing sensory impressions that, it appears, occur in our neural apparatus and visual cortex, both objects and means consistently. However, both the "evil genius"/Matrix and the solipsistic solutions exist as an eternal counterexample against assertions that we can be certain of what external reality REALLY is.
Given that, there has never been any good reason (post 1930s) to doubt the "reality" (objective existence) of a wavefunction, any more than there is good reason to doubt the reality of the electron in a wavefunction or the atom made out of the electrons and so on. By this I don't mean that we can't and don't continue to doubt -- I mean that in the near infinity of possible notional "alternative explanations" for all of the experiments and observations we make about "reality", the simplest solution that best fits the facts has long, long been that wavefunctions are as real as anything else -- they are a provisional truth in excellent agreement with experiment and consistently connected with an entire system that works pretty well.
Can we be certain that it is correct? Of course not. But no reasonable person has been able to doubt their reality more than the alternative explanations, as the alternative explanations have little explanatory power and or usually openly inconsistent in one place or another. Most of the objections are predicated upon our essentially classical everyday experience and the fact that our brains are evolved to optimally "think" classically, but it has long been known that quantum mechanics is as logically/mathematically consistent as classical mechanics -- indeed, if you read Schwinger's lovely "Quantum Kinematics and Dynamics" you can see the precise point where the worldview diverge, from the purely common sense description of measurement processes as an abstract algebra.
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Bell's theorem's implication is that their are not "hidden variable" theories that can explain quantum mechanics.
Wrong. Bell's theorem's implication is that there are no local hidden variable theories which can explain quantum mechanics. Non-local hidden variable theories are not excluded by Bell.
I'd even go one further -- it isn't clear what Bell's theorem implies as soon as you make quantum mechanics properly relativistic and time reversible within a closed physical universe, so that the measurement process it relies on no longer involves entropy in the form of an uncontrolled interaction with a classical measuring apparatus in an unknown microstate. In other words, Bell's theorem is completely meaningless as far as the nature of the actual state or nature of the Universe is concerned; it at best describes a theory of time-ordered, entropy based, projective measurements on open quantum subsystems.
As far as that is concerned, how could one NOT interpret the wavefunction as being "real" (given that a rather lot of it is imaginary if not quaternionic or a number in a generalized geometric division algebra of higher grade:-). It's no more real or less real than any model of a postulated external reality based on our sensory impressions and data, reinforced by reason-based statistical inference.
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(Yeah, yeah, I get it, they are really just trying to say that "time-ordered phenomena apparently exist so the wavefunction must be real", but why bother?. Did any physicist for the last sixty years or so ever doubt this? Should they have, any more than they doubt that reality itself is real and we aren't really all power units in The Matrix?)
Well, yes, I did think about that possibility as well, especially robots with certain useful, ummm, "attachments". Or features. Or whatever. But really, ho-bots are not news; they have been readily available for decades at least with every bit as much intelligence as the real thing.
Well, perhaps $1000 per row -- as I noted at the end, it might be better to build a large hoebot capable of doing 20 rows at once with a single brain. The issue of batteries vs solar (or some mix of the two) would have to be worked out on a cost-benefit basis. Assuming 20 rows 1 meter wide (each), one could cover the entire unit with 10KW worth of cells fairly simply, which gives you more than enough energy to move forward at a steady crawl and perform both the computational and cultivational tasks. That's half the budget of a $20K machine. You're right, even $1000/row might be an underestimate, but it's all capital investment with a potentially long amortization and substantial cost savings (no need to buy expensive chemicals and expensive machinery to safely dispense those chemicals). Those aren't cheap either, and they are an annual expense that leaves you at the mercy of the big agrichemical companies and the manufacturers of farm equipment and various inspectors and the risk that one day somebody will discover that the insecticide you are using causes birth defects or the like and force you completely alter your farming methodology and repurchase capital equipment and shift to yet another chemical (that is without doubt going to be more expensive). Also, mass production should improve economy of scale.
I really don't think it will cost $200K for a production hoebot capable of doing 20 row swatches at a rate of a few meters a minute -- that's more what I would expect to spend building a prototype by hand out of over the counter materials. $10-20K for solar cells and battery backup. Some hefty electric motors for primary motion. Over the counter "robot arms" with a small rotary cultivator on the end and a cheap USB CCD binocular camera. A simple, lightweight PVC "trestle" to connect the brain to the per-row wheels and cultivator units, provide channels for the control wiring, and support the solar array. I actually think it would be pretty bone simple to build a prototype for a hardware budget of $250K (plus whatever sweat-equity in a startup is worth for labor, testing, and coding). I could be wrong, though.
With a prototype in hand, it would then be straightforward to redesign it to be cheap and mass-producible, which ought to cut costs by quite a bit...
A fun idea to play with, anyway.
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Uh, that would be "Pohl". Sorry.
... from The Space Merchants by Pohn and Kornbluth, or would that really be a thinly disguised attempt to rename SoyLent Green...
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No. Of course not. Don't be silly. Is this question really some sort of joke?
The article misses the long term point. One day a small team of farmbots can and will replace both herbicide and insecticide and, to some extent, fertilizer. Powered by the sun, they will spend all daylight hours simply moving up and down the rows of desired plants, distinguishing them from non-desired plants by AI, and using very simple tools to remove/kill those plants. They will similarly be able to identify and kill or spot treat various undesireable "bugs" and other parasites or diseases. They will be able to do things such as loosen the soil above the root masses of the plants to permit optimal penetration of water, precisely mulch and/or fertilize each plant, replant seedlings as they die in the early going so that the field is optimally productive, and quite possibly will be able to deliver just enough water to plants to keep them healthy during at least moderate droughts.
A farmbot capable of all of these things, powered by solar cells, shouldn't cost more than $1000 in a production (not research) environment. The computer guts for it are all cheap by now. It's little more than a Roomba repurposed to "vacuum" down the rows of a field (and hardened against the elements). The hard part is just writing the software, and that's all one time capital investment. A single month's worth of work from one would likely pay for it in reduced labor and chemical costs, not to mention the price premium for "organic" food as more and more people recognize that dumping chlorinated hydrocarbons and neurotoxins onto our food year after year is probably not a really stellar idea.
This may not happen this year, or even this decade, but I think that it is very likely to be coming. Perhaps this startup won't make it. Perhaps it will, using modest success with this very humble precursor to fund gradual improvements until they achieve it. But humans haven't the patience to do the kind of work that a farmbot will do, not at any price, neither domesticated nor imported. Tireless, working from sunup to sundown, processing order of meters of row per minute it will be able to keep one or more acre of planted crop "perfectly" productive without the use of chemicals or far more expensive human time.
Oh, it may not be configured LIKE a roomba as a single crawler -- it may be more effective to build it as (for example) a single brain in a larger, more expensive chassis that can process ten or twenty rows at a time (plenty of cycles to accomplish this in a single central computer, especially with multiple cores). But it's coming.
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