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The Schrodinger Equation

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The goal of materialists is to reduce mind to biology, biology to chemistry, chemistry to physics, and physics to mathematics; they have obviously made considerable progress. At the very bottom of this chain, however, lies quite a surprise–the Schrodinger equation of quantum mechanics. A mathematics text I am reading states that the Schrodinger partial differential equation explains, in theory, all of chemistry, but must be viewed as “an axiom…rather than as an equation that can be derived from simpler principles.”

In an n-particle system, whose potential energy (due to the electromagnetic, gravitational, and strong and weak nuclear forces between these particles) is given by V(x1,y1,z1,…,xn,yn,zn), the probability (per unit volume) of finding particle 1, of mass m_1, at (x1,y1,z1) and particle 2 at (x2,y2,z2), etc., is given by |U|^2, where U is the complex-valued function which satisfies the Schrodinger equation:

-2ihU_t = h^2/m_1(U_{x1,x1} + U_{y1,y1} + U_{z1,z1}) + …
+ h^2/m_n(U_{xn,xn} + U_{yn,yn} + U_{zn,zn}) + 2*V*U

Now when we hear the word “probability”, we think of something like a coin toss, where as a practical matter we cannot do more than state the probabilities, but we assume that in theory we could predict the exact outcome if we only knew more about the initial conditions, wind velocity, and so forth. This is not what is meant by probability here–knowing more will not help! If we send an electron beam with many electrons through a barrier with two slits, the Schrodinger equation does a very good job of predicting the overall distribution when they hit a plate on the other side, but it simply cannot be used to predict where a particular electron will hit. And if quantum mechanical theory is correct, it will never be possible; the laws of physics now give us “probabilities” and nothing more! British astronomer Sir Arthur Eddington said that quantum mechanics “leaves us with no clear distinction between the natural and the supernatual.”

At the macroscopic level, quantum mechanics reduces to classical (Newtonian) mechanics, and when we throw a baseball, the odds are astronomically high that it will obey these classical laws accurately. But if it suddenly stops in mid-air just before Alex Rodriguez swings, it would not really be violating any now-accepted laws of physics, just doing something extremely improbable. If one Red Sox fan says “what incredibly good luck”, and another says “God wanted Alex to strike out”, science simply cannot say which theory is correct. However, if there really is no wind or other force which could explain the sudden stop in terms of classical physics, the “good luck” theory would not impress me, despite obvious problems with the “divine intervention” theory.

Similarly, if a soup of organic chemicals suddenly organizes itself into the first living thing, or if a reptile produces a mammalian offspring, we do not need to conclude that any laws of science have been violated, only that something has happened which these laws tell us is extremely improbable. Science leaves us free to draw the obvious philosophical conclusions from such improbable events, as I have done here .

Thus as the materialists attempt to reduce everything to matter in motion, they discover to their dismay that at the very bottom, controlling the motion of matter, is a remarkable equation which pratically screams, “science is a useful and entertaining tool, but it does not have all the answers.”

By the way, in a previous (Sept 30) post I addressed another interesting and related question, with implications for ID: why on Earth should particles obey an elegant, complex-valued(!!), mathematical wave equation?

Scholasticism (think school) is mainly the attempt to turn philosophy and ultimately all things into a tautology or formal arrangement of information. The problem is that this kind of a system forgets that some things are not communicable and all things are ultimately incomplete except for perhaps in out own minds. The formalization of philosophy is a lot like burning a CD- once you begin to transfer information from one place to another you loose information in the process- The tautological nature of scholasticism is ultimately an attempt at running a command economy of philosophy- It is always incomplete and leaves out very important negations and half thoughts or ideas that exist, as Locke called, "to be and not to be at the same time." Scholasticism is ultimately the Marxism of philosophy- and goes quite handedly with methodological materialism in its desire to drown out free thought - even as it fails to grasp the simplest of concepts like relativistic interpretation - analogy - incompleteness and induction. All things are ultimately to our best senses “inductive” and hence the deductive nature of scholasticism puts to much focus on the material and leaves not enough room for divergent interpretations and insights. However not to say that it wasnt useful- there was great thought in the scholastic movement peaking in the 13th and 14th centuries - in the late 1200s Thomas Aquaintas is said to fomalize the understanding of the nature of God beyond any other efforts up to that time. Frost122585
Addendum: Shazard, I just realized I may have read your comment incorrectly. By "produce exactly such values", did you mean "exactly" as in producting exact values, or "exactly" as in the same as in producing the indeterminancy as QM? One of those those options could negate part of my response! Q
Shazard in 23 stated "I have one interesting hypothesis. What “random” actually means is - “unknown casualistics”. In other words we dont now why the heck the value is this and not that." Since this is about quantum mechanics, it should be possible to link your concept of "unknown causalities" to quanum mechanics. You could link "causalities" to energy, position, time, or momentum, or even something more abstract. My vote is that your notion of causality would represent either transfer of momementum or energy (which are two facets of the same thing in QM.) "Unknown", in your claim, fits nicely with the indeterminancy, or probabalistic, elements of QM. In other words, your argument of "unknown causalities" seems to be a restating of the tenets of quantum mechanics. Shazard also claims "Funny thing is that intellect can produce exactly such values viewed from other point." Umm, if so, could you explain how? QM, as it stands, makes no exceptions. How can intellect produce values more accurate in the observable world than the observable world can support? If the claim isn't reconciled with the observable world (and we know that the phenomenon of quantum mechanics is observable), then your claim about intellect doesn't gibe. Q
allanius #25: And that's the problem of Scholasticism: it laid the ground for the rise of Idealism in reaction to the steadfast "realism" of Scholasticism. Let's hear it for neo-Platonism!!! PaV
DaveScot: You are probably aware that Scholasticism presents a worldview not entirely unlike the one you've described. It requires a fundamentally different notion about the nature of reality from modern scientific materialism, but it could be called a type of "materialism" in the sense that it is opposed to skepticism about the reality of matter, as seen in Idealism. allanius
SH: RE: in general it is impossible to know if it is rnd or product of Intellect and Order The first basic problem with this is that you are forgetting the impact of not only complexity but specification. For, functional states in the relevant senses are utterly rage in the associated config space, especially where we have information-bearing codes to deal with such as in DNA. Codes must be unambiguous, within very tight tolerances, even with provision for error correction. The resulting functionally specified complex information, the relevant subset of CSI is such that random walks starting from arbitrary initial points in the overall relevant config space [e.g of macromolecules in prebiotic soups of any reasonable composition], will by probability exhaustion, be unable to access the fringes of functionality islands fro any naturally occurring hill-climbing algorithms [as NS is claimed to be] to get to work. Cf my always linked app 1 section 6 for an illustrative thought experiment. The second basic problem is that you are forgetting our longstanding familiarity with cause and effect. We are familiar with random processes, with natural regularities flowing from mechanical necessity and with agency. We know how they may work together in given situations. And we reliably know that agency can do what neither of the first can do. Making FSCI-bearing systems is an example of that. Third, you are issuing a promissory note -- trust me, I will in future come up with something else to get away from agency. Pardon us for nbot being willing to put faith in what we do not see here, in favour of what we have routinely seen. Namely, for instance (from my always linked):
CASE STUDY ON CAUSAL FORCES/FACTORS -- A Tumbling Die: For instance, heavy objects tend to fall under the natural regularity we call gravity. If the object is a die, the face that ends up on the top from the set {1, 2, 3, 4, 5, 6} is for practical purposes a matter of chance. But, if the die is cast as part of a game, the results are as much a product of agency as of natural regularity and chance. Indeed, the agents in question are taking advantage of natural regularities and chance to achieve their purposes! This concrete, familiar illustration should suffice to show that the three causal factors approach is not at all arbitrary or dubious -- as some are tempted to imagine or assert.
So, on inference to best, provisional current explanation anchored to empirical observation and experience -- what science rests on in the end -- we hold that reliably FSCI is the product of agency. Kindly provide a counter-example, and we will surrender that bold, falsifiable claim: observed caused phenomena trace to patterns resting on chance, necessity or agency. Just as: provide a suitable perpetual motion machine and thermodynamicists will surrender energy conservation, the second law and the third law. GEM of TKI kairosfocus
I have one interesting hypothesis. What "random" actually means is - "unknown casualistics". In other words we dont now why the heck the value is this and not that. Funny thing is that intellect can produce exactly such values viewed from other point. In other words if we do not know where does numbers 1415296 comes from, they can seem to be random. But intellect and even very good order can produce such strings of numbers and this means exactly very specific order not Random. Random is due to lack of information. So in general, we can't be sure if quantum states of particles is really random stuff coming from some unknown source or it is just unknown software running and we look on the values just like we are looking onto number PI digits without knowing what this number really means. So in general it is impossible to know if it is rnd or product of Intellect and Order Shazard
Geoffrobinson, in 20, said "Quantum mechanics doesn’t give you uncaused causes of free will. It may simply mean we can’t predict things." Quantum mechanics says more than we can't predict things. It says that nothing surrounding those things can predict or respond in a purely deterministic manner. It's not just us, and it's not just predict. A quantum in that tree over there can't deterministically sense when it will be hit by the approaching electron, and it can't respond deterministically, either. That is, it can only sense some time interval in which the collicion probably occurs (the delta T in Heisenberg's equation), it can't sense exactly where it was when it was hit (the delta x in H's equation), it can't sense exactly how much enery it gained (the delta E in H's equation) and its response will be within some probable range of values (the delta-P for momentum in H's equation.) Q
I agree with #15. Quantum mechanics doesn't give you uncaused causes of free will. It may simply mean we can't predict things. geoffrobinson
i wasnt clear on what you said until after i wrote my reply- we agree- but im not sure that we are part materialistic- like decartes thought- i am sort of the beelife that we are a unique part of the univerdal or holly spirit anf thatt he material world id more or less a shell that we move with in the physical laws that permeat through nature - the probabilist view comes into my view in that there is another road within one road ( agreed we are dichotomos) yet the physical world is for me not the true reality but merely a dark reflection of it. Frost122585
Frost122385 Hey - I believe in (compatabilistic) freewill (ie the Calvinist type), don't get me wrong here. And I agree with you and have often reflected upon the micro/macro analogy you gave. Personally, I believe we are dichtomous beings (ie not purely materialist beings) and our immaterial part interfaces with our matter and hence we have free will. I wasn't very clear and for that I apologize. My main point was is that naturalists tend to use quantum mechanics against Christians to explain that we have free will and that we are not locked into some kinda of LaPlaceian determinism. Assuming we are merely automata, I merely wanted to point out the fact that quantum mech. does not makes us more human vs being robot, just that we are now an unpredictable robot. jpark320
Jpark320,
'Well just b/c matter is unpredictable doesn’t mean human’s have free will per se. It could mean that we are in fact automata just unpredictable automata."
Well this is true- yet think about how the macro world is highly predictable and the micro world is not as predictable- then think about the small electrical impulses in our brains that seem to be involved in our decision making-- maybe free will is a little like this. yet our inability to predict change does not necessarily mean that free will exists. Say God has programmed the particles in advance and hence free will is an illusion- but until we know for sure I find the concept and hope of free will personally rather useful. Frost122585
"If we send an electron beam with many electrons through a barrier with two slits, the Schrodinger equation does a very good job of predicting the overall distribution when they hit a plate on the other side, but it simply cannot be used to predict where a particular electron will hit."
This equation is much like the Schrödinger’s cat thought experiment. The argument goes back in modern times to Einstein and Heisenberg- relativity and geometrical objective ontology vs probabilistic (many worlds interpretations of the true nature of things. Einstein IMOP was right... "God does not throw dice." But I see a great analogy here between the quote above about the Schrödinger equation and information theory and NFL. It seems that the distribution ratio can be likened to the "landscape" of NFL- in other words we can know based on observed empirical experience approximately what to expect and as Gödel pointed out this practical thinking seeps its way into our equations without justification- that we must continue to look at this kind of knowledge as probabilistic and not fully objective. The Schrödinger equation just seems to explain the landscape or distribution but it is based on (as the author states) an axiomatic interpretation of physics, biology, chemistry etc. Schrodinger’s cat to my best understanding is merely a physical expression of the inability of mathematics to "get at" the darkest abysses of rational understanding of the objective universe- especially when dealing in probabilities. Like the cat in the Schrödinger experiment we are mortal and like the problem the experiment elucidates the reality of life is the perceptive possibility that we are indecisive. mathematics is not all of the mind and it is meaningless and undermined without all of the other parts (ethics, morality, spirituality, bleeife, hope love etc) acting and working together towards a meaningful purpose. Einstein when he realized the reality of the special theory of relativity said “he was reading God’s thoughts.” Like quantum probability the relativistic reality of different frames of reference is greatly illuminative in that it shows the “appearance” of a living breathing inexact reality of the object universe- yet predestination remains always left on the table as a possibility and that is why we have, and need, the ability to develop truth through enlightened belief. ID is also based in probabilities. Being that we live in an universe where time appears to flow forwards, the detection of an intelligent agent (by its design) must be done backwards - and this requires that we use the wise yet imperfect tool of probability- yet time also allows us to challenge and weigh the data. ID has had it's day in the court of the unbiased seekers of truth and the design inference still stands tested as empirically correct. Regardless of how any times and way the opposition tries to change ground from biology to physics to mathematics to natural physical philosophy etc - the beat goes on and truth stands strongly in the favor of a universe that is full of design-- Even when challenged against all of the king’s horses and men. We cant take probability too seriously as we don’t know exactly how "probabilistic" a probabilistic universe ultimate is. Nor how deep is its reach. But ultimately everything must answer to the truth of objective experience- “Truth… is like gold; for trail and examination must give it price.” -John Locke Frost122585
Well just b/c matter is unpredictable doesn't mean human's have free will per se. It could mean that we are in fact automata just unpredictable automata. I think using quantum mechanics as a basis for free will is no good, but if it is, b/c of its regularity it seems to be controlled by more Newtonian (predictable) than quantum. jpark320
Way to go Dave Scott in 4! “I’d go crazy if there were absolutly nothing I didn’t know about the entire universe past, present, and future. So the creator figures out a way to end the boredom.” But besides granting free will to humans, why wouldn’t the deity reserve the right for himself to intervene in cosmic history as exigencies ensue from those humans? You suggest “… that the free will of rational man is the only non-deterministic thing in the universe and that it was intentionally invented to keep an otherwise deterministic universe full of surprises for someone that knows absolutely everything else about it.” If human agency can produce surprises then surely the deity will reserve the right to react to those surprises. I’m a religious renegade (and ignoramus too) in that it seems to me that the more theologians attempt to make the deity transcend all limits the more they limit him. Omniscience, as you note, precludes discovery. Rude
Granville's article is another demonstration of the fundamental inseparability of chance and regularity. Granville, in OT, posted "Similarly, if a soup of organic chemicals suddenly organizes itself into the first living thing, or if a reptile produces a mammalian offspring, we do not need to conclude that any laws of science have been violated, only that something has happened which these laws tell us is extremely improbable. " Don't the claims of ID modify his argument? If "a soup of organic chemicals suddenly organizes itself", but the scientifically predicted probability of that happening is below some threshold for a best argument as ID postulates, then the best argument stops being that the organization occured due to the "laws of science". That, or the threshold of the best argument is wrong. If that were the case, then Behe's edge would need to be moved, and/or Dembski's explanatory filter would need to determine more things being caused by chance and less by design. Q
Junkyard Tornado: "There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B, because the universe, including particle A, already ‘knows’ what that measurement, and its outcome, will be.”" I don't know about you, but I have no problem with "superluminal speeds and spooky action at a distance." If the universe was once a singularity, then, intuitively to me, is still has to be monistic at the bottom. (With an unknowable nature.) If that's true, then action at a distance only seems distant to us, and is not to the monistic reality itself. mike1962
DaveScot: "Someone else, perhaps many others, might have surmised that the free will of rational man is the only non-deterministic thing in the universe and that it was intentionally invented to keep an otherwise deterministic universe full of surprises for someone that knows absolutely everything else about it." Partly. For decades, I've held that consciousness is a non-deterministic wild card to spacetime. But I don't hold that consciousness is *in* spacetime, but rather that it interacts with it at the quantum level. As for an onmipotent deity creating this setup to alleviate boredom, I find that idea unsatisfactory. If I were onmipotent, and could choose any state of consciousness, then I would be in a constant state of bliss, and would have no need to create anything in the first place, certainly no use for spacetimes and humans. (This is one reason I reject classic theism.) No, I lean toward the idea that were is a transcendent process that *must* generate individual instances consciousness, and spacetime is the medium through which some of these (you and I) interact temporarily for Some Ultimate End, like where were ultimately belong in the Real Universe. Or this could all be a game for bored supercosmic entities. Who knows. mike1962
by "system", I meant the baseball problem, not the hydrogen problem (one of the few exaclty solvable QM problems) DrDan
Granville, You are right that the energy eigenfunction of the H+ atom is discrete but that the position eigenfunction is continuous. I see you're point that when throwing a ball, the energy eigenfunction may be discrete (though probably very closely spaced) but the position e-function may be continuous. We can't know because, as you said, the system is practically not solvable. DrDan
"Superdeterminism has been raised as an escape route from Bell's theorem, which states that a local hidden variable theory cannot reproduce the predictions of quantum mechanics...John Bell discussed superdeterminism in a BBC interview:
There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the 'decision' by the experimenter to carry out one set of measurements rather than another, the difficulty disappears. There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B, because the universe, including particle A, already 'knows' what that measurement, and its outcome, will be."