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  #51  
Old 01-03-2012, 07:25 PM
whc.03grady whc.03grady is offline
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Originally Posted by Mgalindo13 View Post
There's not a difference, that's my point. You personally may see a difference, but that's a relative point of view. You grew up knowing that the Earth was round and revolved around the sun, so it's logical to you. For someone many years ago , it would be a completely foreign and absurd concept.

Just because YOU think something is weird doesn't make it a fallacy.
If someone can't see that every thing is identical with itself is true now, was true at the time of the dinosaurs, is true at the center of Mars, and is true regardless of how one is brought up, then I can't help that person. To believe otherwise is to abandon rationality, to reject the fruits of scientific inquiry.
  #52  
Old 01-03-2012, 07:42 PM
Exapno Mapcase Exapno Mapcase is offline
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Originally Posted by Mgalindo13 View Post
There's not a difference, that's my point. You personally may see a difference, but that's a relative point of view. You grew up knowing that the Earth was round and revolved around the sun, so it's logical to you. For someone many years ago , it would be a completely foreign and absurd concept.

Just because YOU think something is weird doesn't make it a fallacy.
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Originally Posted by whc.03grady View Post
If someone can't see that every thing is identical with itself is true now, was true at the time of the dinosaurs, is true at the center of Mars, and is true regardless of how one is brought up, then I can't help that person. To believe otherwise is to abandon rationality, to reject the fruits of scientific inquiry.
Mgalindo is completely correct. There is no conceivable reason why the underlying workings of the very tiniest and very largest scales should have any connection at all to our understanding, our "common sense" interpretation of what happens in the middle scales we live in. You only find QM weird because you haven't studied it, you don't understand it, and it contradicts some simplistic and limited view of matter that is a ridiculously minor fraction of the universe.

The only thing that's weird is that we've been able to develop mathematics that in any way describes how the real universe works. That this mathematics doesn't have an easy and glib translation into common English and that it doesn't correspond to mundane reality is the most totally expected thing I can think of.

It really is you who's at issue here. Or rather, it really is that you are merely human that's at issue. Humans never see the quantum world. It is what it is, without regard to any aspect of humanness. The universe is math, not culture. If you find math weird that unfortunately says more about you than it does about math.
  #53  
Old 01-03-2012, 07:46 PM
Mgalindo13 Mgalindo13 is offline
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Originally Posted by whc.03grady View Post
If someone can't see that every thing is identical with itself is true now, was true at the time of the dinosaurs, is true at the center of Mars, and is true regardless of how one is brought up, then I can't help that person. To believe otherwise is to abandon rationality, to reject the fruits of scientific inquiry.
No one asked for your help, you started this thread asking "please tell me where I've gone wrong."

You're not grasping the underlying concepts of quantum mechanics and it's not something that any number posts on an Internet message board can correct.

If you're really committed to understanding the topic there's a bounty of information available online and if you're the self-learning type you can even try OpenCourseWare from MIT that has some great courses/materials on quantum theory.
  #54  
Old 01-03-2012, 08:47 PM
Candyman74 Candyman74 is offline
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Originally Posted by whc.03grady View Post
If someone can't see that every thing is identical with itself is true now, was true at the time of the dinosaurs, is true at the center of Mars, and is true regardless of how one is brought up, then I can't help that person. To believe otherwise is to abandon rationality, to reject the fruits of scientific inquiry.
I think the problem here is that people have tried to explain it to you, but you just reject their attempts to explain it out of hand. All that's left is to advise you to go read up on quantum theory, because our superficial attempts aren't doing the trick - and we can't teach a course in it here (well, I couldn't anyway - I understand the concepts, not the mathematics). It's not that you're after help in where you've gone wrong; you're after an opportunity to tell us where we're wrong.

It's kinda like the My Problems With Relativity thread, where someone thinks he's proved Einstein wrong. He hasn't, but he won't accept that.


In order to refute a theory, you need to understand it first. Otherwise how do you even know what it is you're refuting? I mean, you know you're refuting a 3-sentence description of what quantum mechanics is to you, but quantum mechanics is not a 3-sentence description; it's a million equations, experiments, observations, and fulfilled predictions. Those are what you have to refute, not a soundbyte description you heard; and to refute them, you have to understand them very well indeed. You have to intimately know the equations, what they mean, how they were derived, how they are used. Then you can point out what's wrong with them.

Last edited by Candyman74; 01-03-2012 at 08:48 PM.
  #55  
Old 01-03-2012, 09:04 PM
Animastryfe Animastryfe is offline
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Probably a physicist can fill in the gaps here, but when they first measured the speed of light, it was quite astounding that no matter how you measured it, you got the same number. That is not something that fit into any classical physics scheme.
Ah, I understand now. I was thinking that you were referring to the numerical value of c.
  #56  
Old 01-03-2012, 09:19 PM
Leo Bloom Leo Bloom is offline
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This is an excerpt from an English translation of S's paper The Present Situation in Quantum Mechanics--which can be read in its entirety on line--where the cat first appears. It helps to get to primary sources.

The intro graf helps get things going:
That it is in fact not impossible to express the degree and kind of blurring of all variables in one perfectly clear concept follows at once from the fact that Q.M. as a matter of fact has and uses such an instrument, the so-called wave function or psi-function, also called system vector. Much more is to be said about it further on. That it is an abstract, unintuitive mathematical construct is a scruple that almost always surfaces against new aids to thought and that carries no great message. At all events it is an imagined entity that images the blurring of all variables at every moment just as clearly and faithfully as does the classical model its sharp numerical values. Its equation of motion too, the law of its time variation, so long as the system is left undisturbed, lags not one iota, in clarity and determinacy, behind the equations of motion of the classical model.the .... Inside the nucleus, blurring doesn't bother us.

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
[ital mine]


That the lack of the excluded middle is justifiable is discuused in almost identical language by Heisenberg on page 124 of Physics and Philosophy
(entire book online in PDF).
  #57  
Old 01-03-2012, 09:31 PM
Leo Bloom Leo Bloom is offline
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Originally Posted by Leo Bloom View Post

That the lack of the excluded middle is justifiable and necessary in the real world (in these contexts)--as posted above by a number of people--is discuused in almost identical language by Heisenberg on page 124 of his book Physics and Philosophy
(the entire book is online in PDF).
  #58  
Old 01-03-2012, 09:37 PM
Frylock Frylock is offline
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Originally Posted by Cheesesteak View Post
This is seriously the truth. You cannot rely on everyday logic for Quantum matters.

A simple example is the Double Slit Experiment Scroll down to the first variation "interference of individual particles". The experiment makes all kind of sense until you ratchet down the intensity to where you only have individual particles going through the slits at one time. At that point, they continue to show the same interference pattern, even though there isn't any second particle/photon for it to interfere with. It makes absolutely no sense, but the effect has been known for over 100 years.
It's very surprising (or was anyway) but it's not contrary to logic in any sense I can think of.
  #59  
Old 01-03-2012, 09:39 PM
Frylock Frylock is offline
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I don't think anyone in the thread has argued that excluded middle is violated by quantum phenomena, including superposition.

And it's not.
  #60  
Old 01-03-2012, 11:19 PM
Leo Bloom Leo Bloom is offline
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Originally Posted by Omphaloskeptic View Post
I ...
Of course what's more likely than an inconsistency in logic is that there's been an error in the attempt to translate from physical measurements to physical laws to logical statements; and this is what I think is wrong with your first statement. (This is especially easy to do if you're reading popular accounts, which may not be terribly precise in their use of language.) You say that a cat must be either alive or not-alive (excluded middle), and implicitly count this as two distinct well-defined states exhausting all possibilities. At least one of these two properties is empirically shown to fail in quantum mechanics, however. The usual informal way in which physicists talk about this is to label two particular states of the cat system as "alive" and "dead" and then understand that quantum mechanics allows superpositions of these two states. Now you see that there's not actually a logical contradiction. There are more than two possibilities, so excluded middle does not apply, and "not-alive" is not the same as "dead".

I was reading this. Did I get the wrong end of the stick?
  #61  
Old 01-03-2012, 11:23 PM
Frylock Frylock is offline
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Originally Posted by Leo Bloom View Post
I was reading this. Did I get the wrong end of the stick?
Yes, he said:

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There are more than two possibilities, so excluded middle does not apply, and "not-alive" is not the same as "dead".
.

"Excluded middle does not apply" is not the same thing as "excluded middle is violated." What he's saying (and I agree) is that "dead" turns out not to mean the same thing as "not alive."

Everything is either alive or not alive--S's cat is not a violation of this, nor is anything in quantum theory. For excluded middle to be violated with regard to the characteristic "alive," something would have to be both alive and not alive. This cat ain't that.
  #62  
Old 01-04-2012, 04:46 AM
kombatminipig kombatminipig is offline
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I heard it about a liberal art major, an engineer or physicist and a mathematician (respectively saying "sheeps are white", "at least 20 sheeps are white" and "at least 20 sheeps are white on one side", so showing that the mathematician totally ignores common sense)
I think you're giving mathematicians a poor rap and giving common sense way too much credit. I've heard that joke before, and the punchline is that while the physicist considers himself far more strict than the philosopher by pointing out that he can only make statements about observed facts, the mathematician points out that the physicist has made a leap of faith of his own by assuming that all sheep are unicolor. Physicists strive to adhere to strict mathematics as much as any mathematician. At the same time, there's plenty of math that goes against 'common sense'. Statisticians love examples like the Birthday Problem or the Monty Hall paradox that go against all manner of common sense.
Quaternions are another fun mathematical feature that I've had the pleasure to work with in the past, basically vectors in a four dimensional vector space that can be used to describe direction in three dimensional space regardless of a fixed plane, all using complex number (mathematicians, please correct any mistakes in the previous sentence.) I mean, try and wrap common sense around that?

Screw common sense, is that I'm basically saying.
  #63  
Old 01-04-2012, 06:27 AM
Half Man Half Wit Half Man Half Wit is offline
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First of all, quantum mechanics does not violate classical logic. This is straightforwardly demonstrated through the possibility of so-called 'hidden variable'-interpretations, like Bohmian mechanics. They do have unusual properties (non-locality, contextuality, etc.), and they essentially refer to 'surplus structure', i.e. unobservable stuff that the OP (rightly) has a problem with, but it's always at least possible, if perhaps inconvenient. In such interpretations, one can always reason classically about every observable, and weirdnesses of quantum theory are indeed only apparent, and due to our ignorance of the hidden variables.

Nevertheless, you can also choose to look at quantum theory using a logic different from classical logic; however, in this case, it's not the principle of the excluded middle that goes, but rather, distributivity. This is known as quantum logic (and while it has been proposed that it should replace classical logic as the 'proper' logic, because of the above argument, that doesn't actually follow).

The reason for this is so-called complementarity. Two propositions are complementary roughly if both can't simultaneously be known exactly. This is the basis of the uncertainty principle, which thus provides the classic example of why quantum logic does not distribute. First of all, the principle itself says that the accuracy of both position and momentum can't exceed a specific threshold -- the formalization is typically: ΔxΔp > h, where Δx and Δp are the uncertainties in position and momentum, respectively. One can translate this into the following proposition:

z: The particle's momentum is in the interval Δp, and its position lies in the interval Δx.

Now we can think about the following three propositions:

p: The particle's momentum is in Δp,
q: The particle's position is in Δx1
r: The particle's position is in Δx2

Where Δx1 and Δx2 are just the, say, left and right halves of the interval Δx. Then the following proposition: p ˄ (q ˅ r) (where ˄ denotes the logical and, and ˅ denotes the logical or) is clearly true, because it is equivalent to z, and thus, just a restatement of the uncertainty principle. However, the proposition: (p ˄ q) ˅ (q ˄ r), which is equivalent in classical logic, fails to be true, as both p ˄ q and q ˄ r are false; each asserts a proposition incompatible with the uncertainty principle, e.g. 'the particle's momentum is in Δp and the particle's position is in Δx1', which would mean Δx1Δp < h.

Now it is in this complementarity that the key to superposition lies. Let's say there's a property, which can obtain either of two values (typically, this is a particle's spin along some axis), which is complementary to a similar property (spin along another axis, for example). If the particle thus has a definite spin along one axis, its spin along the other axis must be fully indeterminate -- which means, it must be in a superposition of both possible values. Now Schrödinger's cat just consists in coupling the welfare of a macroscopic being to such a superposition -- in principle, it's a straightforward consequence of the theory.

The superposition is then not of the logical form 'A and not-A', i.e. it's not a violation of the principle of the excluded middle. Rather, if 'A' is 'alive', it's just 'not-A' -- the cat's two-valued property doesn't have a definite value along the alive-dead axis (so it's certainly not alive, but also not dead -- one way of viewing this is simply that alive and dead don't exhaust the possibilities in the quantum world, but one can get rather tangled up thinking about it this way).

It's interesting that almost all of quantum theory follows from the existence of complementary propositions -- the way you can 'build' ordinary probability theory on classical logic, you can build quantum mechanics on quantum logic, too. I've written up a sketch of how this works (it will contain a lot of redundancy if you're familiar with classical logic, set theory, and probability, so you can probably skim those parts), and also of how thinking about quantum mechanics in terms of such a novel theory of probability illustrates the origin (and meaning) of interference effects, such as in the classical double slit experiment. And for the complete three-fer, I discuss superpositions in the beginning of this bit on quantum entanglement in the light of what's known as 'Zeilinger's principle' (who, in a word, considers the origin of complementarity to be the finiteness of information in any given system -- once something about it is known perfectly, there simply isn't enough information to decide its other properties). In the interest of openness, however, I should mention that my perspectives probably can't be considered entirely mainstream.

So much for shameless self-promotion...
  #64  
Old 01-04-2012, 08:49 AM
Frylock Frylock is offline
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Originally Posted by Half Man Half Wit View Post
z: The particle's momentum is in the interval Δp, and its position lies in the interval Δx.

Now we can think about the following three propositions:

p: The particle's momentum is in Δp,
q: The particle's position is in Δx1
r: The particle's position is in Δx2

Where Δx1 and Δx2 are just the, say, left and right halves of the interval Δx. Then the following proposition: p ˄ (q ˅ r) (where ˄ denotes the logical and, and ˅ denotes the logical or) is clearly true, because it is equivalent to z, and thus, just a restatement of the uncertainty principle. However, the proposition: (p ˄ q) ˅ (q ˄ r), which is equivalent in classical logic, fails to be true, as both p ˄ q and q ˄ r are false; each asserts a proposition incompatible with the uncertainty principle, e.g. 'the particle's momentum is in Δp and the particle's position is in Δx1', which would mean Δx1Δp < h.
We've talked about this before, of course. Here I'll just note that as far as I can tell (still) z is not equivalent to p ˄ (q ˅ r) unless the particle has a definite position, which, according to mainstream quantum mechanics, it does not.

More specifically, I don't think there's an equivalence between:

P: The particle's position is in delta-x

and

Q: The particle's position is in delta-x1 ˅ The particle's position is in delta-x2.

For P's being true does not require that the position have any property of being in any smaller interval than x. The position is spread out, in a sense, over the whole of x.
  #65  
Old 01-04-2012, 09:07 AM
Frylock Frylock is offline
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Similarly, the statement "Line segment X is in interval [a, c]" does not require that it be true that "either line segment X is in interval [a, b] or line segment X is in interval [b, c]" (where, of course, b is in between a and c).

As far as I can tell, the sense of 'the particle's position' which makes your statement z true in QM is better modeled by line segments than points.
  #66  
Old 01-04-2012, 09:35 AM
Half Man Half Wit Half Man Half Wit is offline
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Similarly, the statement "Line segment X is in interval [a, c]" does not require that it be true that "either line segment X is in interval [a, b] or line segment X is in interval [b, c]" (where, of course, b is in between a and c).
I think it's somewhat misleading to use the 'either... or' construction here, as the logical or is inclusive; so 'line segment is in interval [a, b] or [b, c]' can well be viewed as 'true' if (a part of) the line segment is in [a, b] and (a part of) the line segment is in [b, c], i.e. if it's false that the line segment is not in [a, b] and also false that the line segment is not in [b, c]. Of course, it's not really a good way of talking about quantum mechanics to say things like 'the particle is partially in [a, b]', but it's certainly right that it is unambiguously false to say that the particle is not in [a, b].

Nevertheless, the failure of the distributive law in quantum logic is, as far as I can tell, the accepted view (that's at least how it seems to be regarded both by wiki and the Stanford Encyclopedia of Philosophy), so I think it's the appropriate position for GQ.

Also, particle positions are not really well-modeled by lines, since in measurement, one can measure them arbitrarily well (at the expense of arbitrarily bad knowledge about momentum), which would be impossible for extended objects. The bottom line is that there's really no unambiguous structure 'behind' the quantum formalism, not one of points, and neither one of lines -- there's a lattice of propositions about these properties, which happens to be non-distributive.

Last edited by Half Man Half Wit; 01-04-2012 at 09:40 AM.
  #67  
Old 01-04-2012, 10:09 AM
Frylock Frylock is offline
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To be clear, by "in" I meant "contained entirely within."

As for the mainstream status of the view, note the article you linked to does not claim that QM violates distributivity. It says some philosophers have thought so, while (it seems to me) being careful to neither reject nor endorse this view. And it says that there are non-classical logics which do not validate a theorem we might recognize as encapsulating a "distributive property," and which model QM well. But none of that means QM violates distributivity.
  #68  
Old 01-04-2012, 10:11 AM
Frylock Frylock is offline
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Originally Posted by Half Man Half Wit View Post
Also, particle positions are not really well-modeled by lines, since in measurement, one can measure them arbitrarily well (at the expense of arbitrarily bad knowledge about momentum), which would be impossible for extended objects. The bottom line is that there's really no unambiguous structure 'behind' the quantum formalism, not one of points, and neither one of lines -- there's a lattice of propositions about these properties, which happens to be non-distributive.
That's fine, but it doesn't mean QM "violates distributivity." In particular, the three propositions you offered, if interpreted consistently, validate Propositional Logic's distributive property rather than violating it.

Last edited by Frylock; 01-04-2012 at 10:13 AM.
  #69  
Old 01-04-2012, 10:18 AM
Frylock Frylock is offline
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Put yet another way (sorry): The fact that subtraction isn't commutative doesn't mean that the physical phenomena we model through subtraction "violate commutativity." It doesn't mean that somehow the commutative properties of addition and multiplication are false or invalid.

Similarly, the fact that quantum logic isn't distributive doesn't mean that the phenomena modeled by quantum logic "violate distributivity." It doesn't mean that somehow the distributive properties of the "and" and "or" of propositional logic are false or invalid.
  #70  
Old 01-04-2012, 10:28 AM
BigT BigT is offline
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Originally Posted by Half Man Half Wit View Post
First of all, quantum mechanics does not violate classical logic. This is straightforwardly demonstrated through the possibility of so-called 'hidden variable'-interpretations, like Bohmian mechanics. They do have unusual properties (non-locality, contextuality, etc.), and they essentially refer to 'surplus structure', i.e. unobservable stuff that the OP (rightly) has a problem with, but it's always at least possible, if perhaps inconvenient. In such interpretations, one can always reason classically about every observable, and weirdnesses of quantum theory are indeed only apparent, and due to our ignorance of the hidden variables.
THANK YOU for finally actually answering the question. Or at least starting an answer. It's infuriating watching so many people say that quantum theory somehow disproves classical logic.

What no one seems to be addressing is that we are dealing not with quantum mechanics, but with the Copenhagen interpretation of said mechanics. That particles exist in a superposition that collapses upon measurement is not something that has been scientifically proven, and the OP is right to reject that it has been.

The interpretation of quantum mechanics is the realm of philosophy, not science. There are many interprettions of what is going on. In particular, whether a superposition is a mere mathematical entity or an actual value is hotly debated. Or to put it in the terms of the paradox: whether the cat alivedead, or is its value merely undetermined is actually an open question on the quantum level.

And let us not forget that there is no theory of everything, so even asserting that quantum mechanics is true is not without peril. In fact, many physicists refuse to do anything but say that quantum theory works, and even refuse to interpret the results.
  #71  
Old 01-04-2012, 10:53 AM
Half Man Half Wit Half Man Half Wit is offline
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Originally Posted by Frylock View Post
Similarly, the fact that quantum logic isn't distributive doesn't mean that the phenomena modeled by quantum logic "violate distributivity." It doesn't mean that somehow the distributive properties of the "and" and "or" of propositional logic are false or invalid.
Well, you'll see that in the beginning of my post, I explicitly stated that quantum mechanics does not violate classical logic; nevertheless, it can be described using a logic different from classical logic, in which distributivity does not hold. That's not controversial; the algebra of Hilbert space subspaces, which can be viewed analogously to the algebra of sets in the classical case, simply is not distributive (more accurately, the projection operators -- sort of the 'membership functions' -- aren't). The structure you get from this has the same properties as what one calls a 'logic' (sans distributivity), so that's what people do.

Again, think about the example in terms of 'empirical semantics', where by 'the particle is in [a, c]' one just means 'experiment will find the particle within [a, c]'. From this point of view, it's clearly true that 'experiment will find the particle within [a, c]', and 'experiment will find the particle within [a, b] or within [b, c]' are equivalent -- one can just check one's measurement records afterwards, and it will always be the case that the particle was found within [a, c], and it will always be the case that the particle was found in [a, b] or [a, c], since it was always found at some point in [a, c], and the union of [a, b] and [b, c] is just [a, c] -- thus it was always found at a point in [a, b] or [b, c].

Or, consider another case, a computer build using a three-valued logic. This does not violate two-valued logic, since one can build a computer using two-valued logic that emulated it; but nevertheless, three-valued logic is an obviously valid and equivalent description (you could just as well use the computer based on three-valued logic to emulate a two-valued logic computer -- neither is any more fundamental).

Again, to be perfectly clear, I don't mean to say that quantum mechanics 'violates' distributivity in that distributivity is now somehow wrong -- fundamentally, distributivity is just a way to regroup symbols on a page, and you can do that according to whatever rules you may want to use. But for quantum mechanics, a set of rules in which distributivity doesn't hold appears to be particularly apt, because it models complementarity well. You can use classical logic for the task -- see the first paragraph of my first post in this thread --, but one can argue against this on different grounds (Occam's razor is sometimes put to this task); you can also use three-valued logic (as Reichenbach did), or fuzzy logic, or nonlinear logic, or other kinds of rules one might come up with. There is just no one true right system handed down from above, its rules set in stone -- we have to make do with what we can come up with (and that's a good thing, because if there were one true set of rules, where'd they be supposed to come from?).
  #72  
Old 01-04-2012, 11:59 AM
Frylock Frylock is offline
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Originally Posted by Half Man Half Wit View Post
Well, you'll see that in the beginning of my post, I explicitly stated that quantum mechanics does not violate classical logic;
I did see that, but I guess I was confused about your position. Later on you said

Quote:
...the following proposition: p ˄ (q ˅ r) (where ˄ denotes the logical and, and ˅ denotes the logical or) is clearly true, because it is equivalent to z, and thus, just a restatement of the uncertainty principle. However, the proposition: (p ˄ q) ˅ (q ˄ r), which is equivalent in classical logic, fails to be true, as both p ˄ q and q ˄ r are false; each asserts a proposition incompatible with the uncertainty principle, e.g. 'the particle's momentum is in Δp and the particle's position is in Δx1', which would mean Δx1Δp < h.
which appeared to me to be making a point that classical distributivity is violated by quantum phenomena. But is that not what you're saying here?

Last edited by Frylock; 01-04-2012 at 12:00 PM.
  #73  
Old 01-04-2012, 12:31 PM
Half Man Half Wit Half Man Half Wit is offline
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Well, you could translate what I wrote into classical logic, using for example a hidden variable theory, where particles simultaneously do have a well-defined position and momentum, and we're just prohibited from finding them out. Thus things only appear to be non-distributive due to conspirative dynamics that keep us from accessing the basement layer, which is classical and distributive -- this would essentially amount to emulating quantum logic within classical logic. (Something like this was done, for example, by Edward Moore in his somewhat famous paper 'Gedanken-Experiments on Sequential Machines', where he used automata nowadays called 'Moore machines' to construct an analogue of the uncertainty principle.)

But you can just as well not do that, and just use quantum logic, and only the properties and relations between them quantum mechanics dictates; for those, it is indeed the case that distributivity does not hold, meaning that classical logic, without 'embellishments', just isn't the right tool to do the job of modelling the behaviour of quantum systems (which does not mean that it's wrong anymore than the insufficiency of real numbers to model quantum dynamics means that the real numbers are 'wrong'; this kind of question is just not an empirically decidable one).
  #74  
Old 01-04-2012, 01:07 PM
Mgalindo13 Mgalindo13 is offline
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THANK YOU for finally actually answering the question. Or at least starting an answer. It's infuriating watching so many people say that quantum theory somehow disproves classical logic.
After reading through the posts again I don't really see anyone stating that quantum theory disproves classical logic. I think everyone was trying to inform the OP that standard reasoning (and physics) don't always apply in the quantum world.

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Originally Posted by BigT View Post
What no one seems to be addressing is that we are dealing not with quantum mechanics, but with the Copenhagen interpretation of said mechanics.
I thought that was pretty well understood since the OP was specifically asking about Schrodinger's cat.

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Originally Posted by BigT View Post
That particles exist in a superposition that collapses upon measurement is not something that has been scientifically proven, and the OP is right to reject that it has been.
The term "scientifically proven" is marketing jargon and has nothing to do with the work of real scientists, especially in the realm of physics. This kind of statement is what leads people to saying things like "evolution is only a theory."

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Originally Posted by BigT View Post
The interpretation of quantum mechanics is the realm of philosophy, not science.
There is a plethora of experimentally verified phenomena in this field. Spend five minutes researching entanglement and you'll understand that while physicists disagree about things like what a grand unified theory will look like, there are still widely accepted theories in the community.

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Originally Posted by BigT View Post
Or to put it in the terms of the paradox: whether the cat alivedead, or is its value merely undetermined is actually an open question on the quantum level.
People are far too concerned with this alive-dead cat. This thought experiment was NOT intended to be a way to explain the Copenhagen interpretation to people. It was actually an illustration of the differentiation between the quantum world and our everyday interactions.
  #75  
Old 01-04-2012, 05:19 PM
leahcim leahcim is offline
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Quote:
Originally Posted by BigT View Post
What no one seems to be addressing is that we are dealing not with quantum mechanics, but with the Copenhagen interpretation of said mechanics. That particles exist in a superposition that collapses upon measurement is not something that has been scientifically proven, and the OP is right to reject that it has been.
I do not believe that there is anything about the Schrodinger's cat concept that is tied uniquely to the Copenhagen interpretation. Certainly Many-Worlds interpretation still has the alive/dead cat, and just adds to it by making the observer a lookingatalivecat/lookingatdeadcat entity once the box is opened.

Hidden variable interpretations get rid of the superposition, but replace it with quantities that are subject to the same criticism that the OP makes about the superposition itself -- that we're introducing these fundamentally non-observable things. (Plus, due to Bell's theorem, they need to be non-local, which buggers up relativity, too).
  #76  
Old 01-04-2012, 07:33 PM
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Originally Posted by leahcim View Post
I do not believe that there is anything about the Schrodinger's cat concept that is tied uniquely to the Copenhagen interpretation. Certainly Many-Worlds interpretation still has the alive/dead cat, and just adds to it by making the observer a lookingatalivecat/lookingatdeadcat entity once the box is opened.

Hidden variable interpretations get rid of the superposition, but replace it with quantities that are subject to the same criticism that the OP makes about the superposition itself -- that we're introducing these fundamentally non-observable things. (Plus, due to Bell's theorem, they need to be non-local, which buggers up relativity, too).
But it's not that bad. A simple solution has been staring physicists in the face for decades, has been mentioned by luminaries like Wheeler and Feynmann, and avoids the Bell's Paradox completely!

I'm untrained but I hope any response to me here is a serious refutation, not a frivolous comparison with "purple cows."

In the Bell's paradox, twin photons are created on Monday, then read Tuesday and Wednesday on distant asteroids. Note that the Tuesday is not preferentially "earlier" than the Wednesday reading, since each is outside the other's cause-effect cone. Yet in the Paradox, the reading on one asteroid seems somehow telepathized to the other asteroid, faster than light, or even Wednesday's filter setting can be seen to affect Tuesday's reading.

The paradox disappears if you consider that the paired photon is a single photon, arriving from some future point beyond the Wednesday asteroid, travelling backward to the actual pair creation event, then forward in time to Tuesday's asteroid. Cause-effect behaves trivially: Wednesday's filter setting is imparted to the photon, and the polarization is "later" detected by the Tuesday receiver.

Is there a flaw in this argument? Wheeler-Feynmann argue, IIRC, that reverse-causality photons of the type described imply "advanced" radiation waves whereas only "retarded" radiation waves are observed. On the other hand, wouldn't advanced waves be quite hard to detect? (I am not quite espousing the traditional Transactional model: it has an unnecessarily complex notion of causation, though I won't try to synopsize mine in this post.)

Just as rising entropy is a consequence of the happenstance that we inhabit a world of low entropy, couldn't the prevalence of retarded waves be an artifact of the same thermodynamic state? Probably not, or geniuses like Feynmann would have seized on the elegance of this solution. Still, it would be nice to understand where the model fails.
  #77  
Old 01-04-2012, 11:55 PM
leahcim leahcim is offline
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Quote:
Originally Posted by septimus View Post
The paradox disappears if you consider that the paired photon is a single photon, arriving from some future point beyond the Wednesday asteroid, travelling backward to the actual pair creation event, then forward in time to Tuesday's asteroid. Cause-effect behaves trivially: Wednesday's filter setting is imparted to the photon, and the polarization is "later" detected by the Tuesday receiver.
Some notes:

(1) I think you are talking about the EPR paradox.

(2) A description that attempts to prevent a causality problem by positing that the information is routinely transmitted backwards in time is somewhat defeating the purpose. If we posit that we can sent information backwards in time, why not just send it between the measurements directly.

(3) The Feynman-Wheeler description of "particles going backwards in time" is a description of antimatter. I.e. that an X with its time-direction reversed is an anti-X. That means your description is fine for entangled photons, or particle-antiparticle pairs, but entanglement is not limited to those kinds of particles. There is nothing in principle stopping an electron from being entangled with another electron, or a proton, or something else, which can't be described the way you have it.
  #78  
Old 01-05-2012, 05:24 AM
septimus septimus is offline
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Quote:
Originally Posted by leahcim View Post
Some notes:

(1) I think you are talking about the EPR paradox.

(2) A description that attempts to prevent a causality problem by positing that the information is routinely transmitted backwards in time is somewhat defeating the purpose. If we posit that we can sent information backwards in time, why not just send it between the measurements directly.

(3) The Feynman-Wheeler description of "particles going backwards in time" is a description of antimatter. I.e. that an X with its time-direction reversed is an anti-X. That means your description is fine for entangled photons, or particle-antiparticle pairs, but entanglement is not limited to those kinds of particles. There is nothing in principle stopping an electron from being entangled with another electron, or a proton, or something else, which can't be described the way you have it.
1. Yes, I think all these "paradoxes" are closely related; indeed are all manifestations of quantum physics' "mysterious" implication.

2. The information doesn't magically travel back in time; it just follows a normal cause-effect relation, but with time-sense reversed. Counterintuitive? Of course. Problematic? Perhaps; I'd like to understand the specific objections. But the beauty of the scheme, if it is at all workable, is that quantum mystery disappears.

3. Au contraire, haven't Feynmann et al themselves modeled electrons as positrons going backward in time?
  #79  
Old 01-05-2012, 09:19 AM
Half Man Half Wit Half Man Half Wit is offline
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septimus, perhaps the discussion of your idea would be something for a separate thread? Personally, I don't see where you differ from Cramer's transactional interpretation, and as with that interpretation, I'm not sure I really see the need. As leahcim notes, interpretational problems of EPR experiments mainly focus on how to save causality in the presence of apparently faster than light 'spooky actions' (which I consider neither spooky nor 'actions' in most senses of the word). To just throw out the notion of causality does seem like cheating somehow. And of course, the problems you get are those you get with any retrocausal proposal, such as paradoxical influences on the past, causal loops (i.e. A caused B retrocaused A), and of course, there's also the problem of how our experience of a unidirectional arrow of time comes about; the usual argument of 'entropy was lower in the past' doesn't work, since for every point in time, if causal influences propagate in both time directions symmetrically, one should expect that entropy is higher both towards the past and towards the future, as the dynamics that generate entropy increase work in both directions equally well.
  #80  
Old 01-05-2012, 11:12 AM
CurtC CurtC is offline
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I think I see where whc.03grady is misunderstanding something...

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Originally Posted by whc.03grady View Post
Science makes statements about the observable (empirical) world. The unobserved particle is, by definition, unobserved. What I'm asking is, on what basis does the quantum physicist get to make the claim that, during the time when it's unobserved, the particle has such-and-such property?
I can see where you get this impression, if you're starting from the Schrodinger's Cat idea. However, we do make observations that tell us about this uncertainty at the heart of the quantum world. Before we observe the particle at the wall behind the two slits, there was uncertainty and it seemed to pass through both slits simultaneously (as a wave). Our observations show us that this happened. Flash memory works because there's uncertainty about the position of an electron, and sometimes they just appear inside an insulator. But we can observe that flash memory works.

Our observations lead us to the idea that these wave/particle things exist in a superposition of states. It's not, like you seem to be saying, that we base these ideas on simple ignorance of what may be really happening.


Quote:
Originally Posted by DrDeth View Post
And of course, the thought experiment *IS* ridiculous, as the cat is a observer.
Further, the Geiger counter that triggered (or not) the breaking of the vial of poison, is itself an observer.

Last edited by CurtC; 01-05-2012 at 11:12 AM.
  #81  
Old 01-05-2012, 04:03 PM
Apathetic Coma Apathetic Coma is offline
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Originally Posted by Reno Nevada View Post
The best answer that I have ever read to this question was of course Cecil's: http://www.straightdope.com/columns/...t-an-epic-poem
Dude, I was just browsing...but that link made me sign up.

Don't worry, I'm good.

  #82  
Old 01-05-2012, 08:51 PM
Candyman74 Candyman74 is offline
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Is if just me, or are the usernames whc.03grady and tomh.4040 reminiscent in style of each other?

One being "I've figured out what's wrong with quantum theory" and the other being "I've figured out that Einstein was wrong about relativity"?
  #83  
Old 01-06-2012, 02:49 AM
Half Man Half Wit Half Man Half Wit is offline
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Quote:
Originally Posted by Candyman74 View Post
Is if just me, or are the usernames whc.03grady and tomh.4040 reminiscent in style of each other?
I don't think so. To me, it seems that whc.03grady has shown himself both more knowledgeable and corrigible on his topic, plus we haven't yet seen any inane thought experiments intended to expose errors in the thinking of some of the smartest people in the world for nearly the past 100 years that can ultimately be reduced to trivial misunderstandings based on biased readings of pop-sci arguments...
  #84  
Old 01-06-2012, 07:58 AM
canterburyales canterburyales is offline
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Many posters have recommended researching the topic to get a better understanding of the strangeness of quantum phenomenon that is being illustrated by the story of Schrodinger's Cat. That is the best approach.
I think the heart of the matter is the difficulty in accepting the quantum view that the world seems to be inherently probabilistic. As a non-physicist I have gotten a lot out of the various Feynman lectures available online.

This series is a good place to start:

http://vega.org.uk/video/programme/45

He talks about the idea of understanding at 20:15.
  #85  
Old 01-06-2012, 01:23 PM
Cartoonacy Cartoonacy is offline
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Originally Posted by Frylock View Post
It's very surprising (or was anyway) but it's not contrary to logic in any sense I can think of.
No? What about

Quote:
Originally Posted by Wikipedia: Double-slit experiment
For example, when a laboratory apparatus was developed that could reliably fire one electron at a time through the double slit, the emergence of an interference pattern suggested that each electron was interfering with itself, and therefore in some sense the electron had to be going through both slits at once — an idea that contradicts our everyday experience of discrete objects.
  #86  
Old 01-06-2012, 07:52 PM
Chronos Chronos is offline
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Fundamentally, Schrödinger's point about the cat was that the Copenhagen interpretation of quantum mechanics led to results which seem intuitively absurd. About that, he's right. But there are many different possible interpretations of quantum mechanics, all of them exactly equivalent in the sense that they predict the same sets of observations, and not all of them lead to that particular absurdity. The tricky part, though, is that all of them lead to their own particular absurdities: Bell's Inequality proves that any model which does not lead to one of a variety of things we consider intuitively absurd, cannot be consistent with the results of the measurements we've actually performed. So somehow or another, there's something about physics that we consider intuitively absurd (which should, of course, be taken as a flaw in our intuitions, not as a flaw in physics), but we can't actually say just what the absurdity is.
  #87  
Old 01-06-2012, 08:07 PM
Leo Bloom Leo Bloom is offline
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Chronos! Where the heck you been, man?
  #88  
Old 01-06-2012, 09:17 PM
clairobscur clairobscur is offline
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Quote:
Originally Posted by kombatminipig View Post
I think you're giving mathematicians a poor rap and giving common sense way too much credit..
No, I understand the meaning of the joke. But in the context of this thread (the OP only willing to accept unicolor sheep), it seemed to me that the emphasis should be on the mathematician (rightly) ignoring common sense. The physicist/engineer knew that the mathematician was right. The OP still struggles with the concept.

I think I'm going to search for some similar jokes. It's been a while since I heard any. Out to find the one about the physicist and the engineer fighting a kitchen fire



ETA : Immediately found some here. The one I was searching for and couldn't remember being the first one. Not really helpful for the OP, but still...

Last edited by clairobscur; 01-06-2012 at 09:19 PM.
  #89  
Old 01-06-2012, 09:34 PM
Chronos Chronos is offline
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Visiting my mom (who has lousy internet access) for vacation. But I'm back in the land of broadband now.
  #90  
Old 01-07-2012, 02:47 AM
Leo Bloom Leo Bloom is offline
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Originally Posted by clairobscur View Post
No, I understand the meaning of the joke. But in the context of this thread (the OP only willing to accept unicolor sheep), it seemed to me that the emphasis should be on the mathematician (rightly) ignoring common sense. The physicist/engineer knew that the mathematician was right. The OP still struggles with the concept.

I think I'm going to search for some similar jokes. It's been a while since I heard any. Out to find the one about the physicist and the engineer fighting a kitchen fire



ETA : Immediately found some here. The one I was searching for and couldn't remember being the first one. Not really helpful for the OP, but still...
It came to me, but I can't remember the first two fields are. (Maybe they're all physicists ...)

Three umpires answering a furious coach:

Umpire 1: I calls 'em what they are.
Umpire 2: I calls 'em as I see 'em.
Umpire 3: They ain't nothin' till I calls 'em.
  #91  
Old 01-07-2012, 04:01 AM
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Why is it so hard to believe that science has proved the existence of zombie cats?
  #92  
Old 01-07-2012, 05:28 AM
Senegoid Senegoid is offline
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Originally Posted by Chronos View Post
Fundamentally, Schrödinger's point about the cat was that the Copenhagen interpretation of quantum mechanics led to results which seem intuitively absurd. About that, he's right.

<snip>

Bell's Inequality proves that any model which does not lead to one of a variety of things we consider intuitively absurd, cannot be consistent with the results of the measurements we've actually performed. So somehow or another, there's something about physics that we consider intuitively absurd (which should, of course, be taken as a flaw in our intuitions, not as a flaw in physics), but we can't actually say just what the absurdity is.
This is the Quantum Meta-Heisenberg Uncertainty Theorem
  #93  
Old 01-07-2012, 12:53 PM
Exapno Mapcase Exapno Mapcase is offline
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It came to me, but I can't remember the first two fields are. (Maybe they're all physicists ...)
Absolute Zero Gravity: Science Jokes, Quotes and Anecdotes, by Betsy Devine and Joel E. Cohen is full of them. If you ever stumble across a cheap copy, grab it. The best science joke book ever.
  #94  
Old 01-08-2012, 04:33 PM
Leo Bloom Leo Bloom is offline
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Originally Posted by canterburyales View Post
Many posters have recommended researching the topic to get a better understanding of the strangeness of quantum phenomenon that is being illustrated by the story of Schrodinger's Cat. That is the best approach.
I think the heart of the matter is the difficulty in accepting the quantum view that the world seems to be inherently probabilistic. As a non-physicist I have gotten a lot out of the various Feynman lectures available online.

This series is a good place to start:

http://vega.org.uk/video/programme/45

He talks about the idea of understanding at 20:15.
Astounding, great great cite.

I can't wait to watch the next three lectures.

Thanks.
  #95  
Old 01-11-2012, 10:34 PM
canterburyales canterburyales is offline
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Originally Posted by Leo Bloom View Post
Astounding, great great cite.

I can't wait to watch the next three lectures.

Thanks.
When you are done with those check this out:

http://research.microsoft.com/apps/t...uva/index.html
  #96  
Old 04-18-2017, 06:13 PM
septimus septimus is offline
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Quote:
Originally Posted by septimus View Post
But it's not that bad. A simple solution has been staring physicists in the face for decades, has been mentioned by luminaries like Wheeler and Feynmann, and avoids the Bell's Paradox completely!

In the Bell's paradox, twin photons are created on Monday, then read Tuesday and Wednesday on distant asteroids. Note that the Tuesday is not preferentially "earlier" than the Wednesday reading, since each is outside the other's cause-effect cone. Yet in the Paradox, the reading on one asteroid seems somehow telepathized to the other asteroid, faster than light, or even Wednesday's filter setting can be seen to affect Tuesday's reading.

The paradox disappears if you consider that the paired photon is a single photon, [or rather a triplet of photon events — the entanglement on Monday, and the detections on Tuesday and Wednesday] ... Cause-effect behaves trivially: Wednesday's filter setting is imparted to the photon, and the polarization is "later" detected by the Tuesday receiver.

Is there a flaw in this argument? Wheeler-Feynmann argue, IIRC, that reverse-causality photons of the type described imply "advanced" radiation waves whereas only "retarded" radiation waves are observed. On the other hand, wouldn't advanced waves be quite hard to detect? (I am not quite espousing the traditional Transactional model: it has an unnecessarily complex notion of causation, though I won't try to synopsize mine in this post.)

Just as rising entropy is a consequence of the happenstance that we inhabit a world of low entropy, couldn't the prevalence of retarded waves be an artifact of the same thermodynamic state? Probably not, or geniuses like Feynmann would have seized on the elegance of this solution. Still, it would be nice to understand where the model fails.
Yes, I realize I provide more questions than answers. But I think my intuitionthat admitting retrocausality is the way Occam would be most delighted to cut with his razor — is sound. Don't lump me with Cramer, please. I read Huw Price. (1. Yes, I know his PhD is not in physics. 2: I had the same intuition before I read Price.)

Quote:
Originally Posted by Half Man Half Wit View Post
septimus, perhaps the discussion of your idea would be something for a separate thread? Personally, I don't see where you differ from Cramer's transactional interpretation, and as with that interpretation, I'm not sure I really see the need. As leahcim notes, interpretational problems of EPR experiments mainly focus on how to save causality in the presence of apparently faster than light 'spooky actions' (which I consider neither spooky nor 'actions' in most senses of the word). To just throw out the notion of causality does seem like cheating somehow. And of course, the problems you get are those you get with any retrocausal proposal, such as paradoxical influences on the past, causal loops (i.e. A caused B retrocaused A), and of course, there's also the problem of how our experience of a unidirectional arrow of time comes about; the usual argument of 'entropy was lower in the past' doesn't work, since for every point in time, if causal influences propagate in both time directions symmetrically, one should expect that entropy is higher both towards the past and towards the future, as the dynamics that generate entropy increase work in both directions equally well.
I neglected to answer Mr. Wit five years ago, so will do so now.

I do not "throw out the notion of causality" nor are there "faster than light actions." Yes, the Wednesday and Tuesday events are outside each others' causality cones, but information can tunnel(!) using the "advanced action" path from detector to entangler at the speed of the electron or photon. I'll agree there are probably severe constraints on what kind of information can be exchanged, but information is manifestly exchanged in the case of EPR and GHZ paradoxes.

Yes, we give up the fixity of time's arrow. But where is that written in stone? In the the 2nd Law of T ΔS≥0 which Mr. Wit mentions in concluding ("causal influences propagat[ing] in both time directions"): I certainly admit the possibility of boundary conditions, just as other models do, e.g. Big Bang Hypothesis, or for that matter 19th century physicists like Boltzmann. It is, apparently, the extremely low entropy at -13 Gigayear — however this boundary constraint arose — which leads to the causality arrow so clearly experienced by human brains. (This much is stipulated, I think, even by some who do not also propose retrocausality.)
  #97  
Old 04-22-2017, 05:17 AM
Half Man Half Wit Half Man Half Wit is offline
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Quote:
Originally Posted by septimus View Post
Yes, I realize I provide more questions than answers. But I think my intuitionthat admitting retrocausality is the way Occam would be most delighted to cut with his razor — is sound.
While I agree that retrocausality furnishes a possible explanation for Bell inequality violation, I don't really agree that it's a more parsimonious solution. For instance, you incur new explanatory burdens: why, if there is retrocausality, can we not actively influence the past? What additional mechanisms prevent chronology violation, or the sending of information into the past, or even to spacelike separated events?

In contrast, in ordinary quantum mechanics, you merely need to give up the assumption that all measurements should obey a joint probability distribution.

Quote:
I do not "throw out the notion of causality" nor are there "faster than light actions."
Well, if there is retrocausality, then either there is the possibility of causes influencing their effects, or there must be a mechanism to prevent this; furthermore, you can produce FTL effects by simply sending a signal to the future, and then sending one to a different point in the past. Indeed, nonlocality and superluminal signalling are really two sides of the same coin, and retrocausation leads at least to effective nonlocality.

Quote:
I'll agree there are probably severe constraints on what kind of information can be exchanged, but information is manifestly exchanged in the case of EPR and GHZ paradoxes.
No. In fact, the No Communication-theorem entails that no information can be transmitted using entanglement alone (any more than information can be transmitted using a setup where each of us has an envelope with a colored card in it, such that yours is red if mine is green, and vice versa; opening your envelope, you'll immediately know the color of my card, but no information has been transmitted). In order to send information, you always have to rely on classical communication

Quote:
I certainly admit the possibility of boundary conditions, just as other models do, e.g. Big Bang Hypothesis, or for that matter 19th century physicists like Boltzmann.
Actually, I don't think there's really a well-posed initial value problem anymore in the presence of retrocausality; seems to me that at minimum, you'd have to also fix some far future conditions; which again entails extra explanatory burdens.
  #98  
Old 04-22-2017, 02:07 PM
Kedikat Kedikat is offline
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I feel that a lot of quantum mechanics is still a manufactured framework to enable people to work in that difficult realm. It has not yet fully reflected the reality of what is going on. I liken it to navigating with two dimensional maps before you know the world is a sphere. You can make it work. But you need to invent rules in order to do it. A little creative math to straighten or curve things to plot the best path that works in the reality that you do not yet know. Many places where there be monsters.

That doesn't mean it does not work. We use flat maps all the time and get where we want to go. Quantum mechanics is a developing map. It helps explore that world. The explorers may at some point see it for what it is. Possibly far outside the boundaries of their map.
  #99  
Old 04-22-2017, 02:45 PM
rat avatar rat avatar is offline
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To clarify for other users due to the use of various terms in this thread.

EPR experiment nor any other quantum experiment has demonstrated that faster-than-light signaling is possible. The lack of transfer of usable "faster-than-light signaling" or what is commonly also called information has not been demonstrated.

Because of this lack of useable information the speed of causality is not violated at this date.

While a lack of a unifying theory may make these paradoxes fairly confusing as there is a significant amount of unsettled science the restriction on the speed of causality is related to communication faster than the speed of light and not other aspects of our universe.

In fact in the future even the expansion of the universe is expected to exceed the speed of light. This does not imply that the particles themselves are superluminal, but that the distances between them will be.

As of this date the no-communication theorem is still firmly in place.
  #100  
Old 04-22-2017, 03:22 PM
rat avatar rat avatar is offline
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Alice and Bob each take one of an entangled pair.
Alice reads the Z spin on one of the entangled pair but Bob doesn't have a way to detect that she did.
Alice can't control what the value is that will be read, she reads a "random value.
Alice my read an up or a down. Bob will read a complement of Alice's "random" value, to Bob it appears random as well.

Bob would need a way to know that Alice has actually performed a measurement or if he is the first one to measure a member of the pair.
Bob's statistics for his particle alone look the same either way. If Alice and Bob are not local to each other they cannot tell if something is random or due to entanglement.

It is easy to confuse tests that do have locality and non FTL communication with thought experiments that describe how entanglement interactions are FTL but to reference Kedikats post remember that most of the math is in done in Hilbert space or other Euclidean spaces and thus will not apply to space like intervals.

While our theories are incomplete, any violation of the speed of causality is purely theoretical and there is no experimental proof for "faster-than-light signaling" but only for "faster-than-light interactions".

I do want to address this from the OP:

Quote:
Originally Posted by whc.03grady View Post
Why does the physicist get to invent a property (the superposition) that is, in principle, unobservable
While others have cited tests for this theory I also wanted to point out that it was recently observed on a physical object.

http://physicsworld.com/cws/article/...visible-object

Last edited by rat avatar; 04-22-2017 at 03:24 PM.
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