Schrodinger's Cat

[Animastryfe]

@whc.03grady

I didn’t take it as rude.

I think I see what you’re saying. So if the mathematician shows that 1+1=3, and that result is confirmed over and over again, then we’re supposed to accept the absurd (or “absurd”) result and maybe give her a prize. I suppose I should’ve said, “Why does physics (meaning the original experimenter and all those who verified the result) get a pass?”

I don’t think you should use this as an example. Mathematics uses deduction based on certain axioms and rules of logic. I do not think there is any a priori reason that, for a certain set of axioms, one cannot make a proof that 1+1=3.

The difference between mathematics and physics in this context is that mathematics is not a ‘science’, in the sense that one does not do experiments to check its results. A mathematician cannot find a proof that 1+1=3 for the mathematics that most people are familiar with, or else we’re in some kind of Lovecraftian universe and any talk of logic or ‘that makes sense’ is moot.

To help us answer your questions about physics, it would be helpful to know your background knowledge of physics. Have you read any textbook on quantum mechanics? I have not read any popular science books on physics for a few years now, but I cannot think of any popular science example of an author explaining quantum mechanics with enough details so that a layman will really understand superposition of quantum states, entanglement and whatnot.

Edit: Well, Omphaloskeptic just wrote what I wanted to write, but with more detail. Darn.

[Wheelz]

One of my favorite explanations of Schrodinger’s Cat was posted right here on the SDMB, so credit where credit’s due:

@Cayuga

Schroedinger made up the story of the cat to say, “If what you’re saying about quantum mechanics is true, then the cat is both dead and alive. That’s obviously ridiculous, so what you’re saying about quantum mechanics must not be true.”

And the quantum greasemonkeys (what do you call comeone who works with quantum mechanics, anyway?) replied. “You’re right. In the large-scale, everyday world it would be ridiculous. But it’s a fact of life in the sub-atomic quantum world. Which is why quantum mechanics is such a bear to understand.”

[WarmNPrickly]

@whc.03grady

The physicist says the cat is in a superposition, viz., is both alive and dead.

Physicists don’t say that. That is the entire point of the thought experiment. To say that the cat is simultaneously dead and alive is pretty ludicrous. I am not aware of any interpretation that does this. Until we open the box, the mathematics treat it as a 50% chance of either.

For one thing, note that, if shown true, neutrions moving faster than light wouldn’t entail an absurdity. It would show that a fundamental proposition about physics was false, yes, but there’s nothing logically impossible about a neutrino, or a '67 Buick Skylark, going faster than light; there’s no absurdity there.

More than likely, if it does turn out that these neutrinos are traveling faster than light, the current understanding of relativity will be slightly modified rather than tossed out as false. In fact, superluminal travel does create something that is logically impossible, but then so did the initial measurements of C. Nevertheless, Newtonian physics largely dominates engineering and designs of modern equipment. Physics adjusts to new information, but it doesn’t toss out the old information as false.

[whc.03grady]

@Omphaloskeptic

It is tempting to view logic and mathematics as basic, with physical laws somehow building on these. But physics is fundamentally an empirical science, not a logical one; if empirical physical results contradict logical derivations then it’s the logic that’s broken, not the physics.

I appreciate the fact that physics isn’t built atop logic in the sense that you describe (though I have other, unexpressed feelings about this that aren’t germane to the topic at hand), and I likely slid into that way of thinking in an earlier post. But it still seems to me that if we’re dealing with something like a miracle here.
I’m thinking of Hume’s treatment of miracles, which in short says (taking his example), which is more believable? That someone rose from the dead after three days, or that everyone’s evidence supporting that occurrence is mistaken? Which does reason compel you to bet on?

The same kind of reasoning seems to apply here: if you had to bet, would you bet that (a) there are cases where contradictions obtain; or (b) the descriptions/interpretations of those cases are in error? Now, it’s clear where I place my money, but I’m curious as to why others might bet differently?

@Omphaloskeptic

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 wonder if you could elucidate on this a bit. First, I don’t see how changing “not-alive” to “dead” makes a difference with respect to there not actually being a logical contradiction. Second, I don’t get how the physicist “understand[s] that quantum mechanics allows superpositions of these two states.” (If I could get a handle on this (and if it’s true, of course!), it might be resolved for me and render the rest of what I’m saying irrelevant.)

What’s more, I don’t see how empirical results can trump principles of logic or reasoning. The whole process of science is built upon certain more or less formal principles of reasoning: “If a theory is confirmed so-and-so many times, we can regard it as true” would be an example. I wholeheartedly agree with this principle, but hopefully we all can see that no experiment has ever, will ever, or could ever be performed to show that it’s a good principle. The scientific process relies quite heavily on the principles of mathematics for instance, principles which themselves are in no way proven by science.

What I’m trying to say in this post is there are certain meta-scientific principles by which science operates that are not themselves provable within science, yet are accepted (NB: I do not take this to mean scientific reasoning is in any way deficient). But why is it that when some results seem to run contrary to a certain principle (non-contradiction), that the impulse in this case is to pitch the principle, not the results?

[Animastryfe]

@WarmNPrickly

In fact, superluminal travel does create something that is logically impossible, but then so did the initial measurements of C.

Please expand on this. What was thought to be logically impossible about C? I assume that by C you mean the speed of light in a vacuum.

[The_Hamster_King]

@whc.03grady

What’s more, I don’t see how empirical results can trump principles of logic or reasoning.

You have it exactly backwards. It’s the success of logic in explaining empirical results that justifies its use.

Depending on the axioms you pick as your starting point, you can construct a wide range of different mathematical systems. You can create a system where 1+1=3 or where TRUE & TRUE = FALSE, if you want.

Now, some of these systems happen to be useful in modelling the behavior of the universe. Systems where 1+1=2 and TRUE & TRUE = TRUE fall into this category.

The reason we trust these systems is because they do a good job of explaining what we observe. However, if we observe things that violate the predictions, then the systems must change.

[Candyman74]

@whc.03grady

What I’m trying to say in this post is there are certain meta-scientific principles by which science operates that are not themselves provable within science, yet are accepted (NB: I do not take this to mean scientific reasoning is in any way deficient). But why is it that when some results seem to run contrary to a certain principle (non-contradiction), that the impulse in this case is to pitch the principle, not the results?

OK, let’s try to narrow it down.
Which scientific principle, specifically, are you referring to? (Schrodinger’s Cat isn’t a scientific principle).
If you could identify which scientific principle it is that you disagree with, at least we’re all on the same page. And perhaps we can discuss the evidence for that principle, or illustrate how it is successfully used in technology, or how it is used to successfully make predictions.

[Candyman74]

@whc.03grady

What’s more, I don’t see how empirical results can trump principles of logic or reasoning.

Of course they can. They* must*. They have to. Otherwise we’d still believe that the sun revolved around the earth. It was our observations - empirical results - which told us otherwise and contradicted the logic and reasoning of centuries of great thinkers.

If your observations are at odds with your reasoning, the flaw is much more likely to be in your reasoning than in your observation. But you test and retest and retest the obvservation over and over and over again to be sure.

[Omphaloskeptic]

@whc.03grady

I appreciate the fact that physics isn’t built atop logic in the sense that you describe (though I have other, unexpressed feelings about this that aren’t germane to the topic at hand), and I likely slid into that way of thinking in an earlier post. But it still seems to me that if we’re dealing with something like a miracle here.
I’m thinking of Hume’s treatment of miracles, which in short says (taking his example), which is more believable? That someone rose from the dead after three days, or that everyone’s evidence supporting that occurrence is mistaken? Which does reason compel you to bet on?

The same kind of reasoning seems to apply here: if you had to bet, would you bet that (a) there are cases where contradictions obtain; or (b) the descriptions/interpretations of those cases are in error? Now, it’s clear where I place my money, but I’m curious as to why others might bet differently?

Well, I’m arguing that there is no logical contradiction, and that your interpretations are in error, so I guess that makes (b), but I think it’s a different (b) than yours since I think you think it’s somebody else’s interpretations that are in error.

There’s a big difference between quantum mechanics and miracles, which is repeatability. Miracles, at least of the sort you’re talking about, are one-time events. This makes them very difficult to consider using the scientific method. With quantum mechanics, you can measure as many electrons as you want; when you always get the answers that quantum mechanics predicts, you may start to think there’s something to it after all, weird or not.

I wonder if you could elucidate on this a bit. First, I don’t see how changing “not-alive” to “dead” makes a difference with respect to there not actually being a logical contradiction. Second, I don’t get how the physicist “understand[s] that quantum mechanics allows superpositions of these two states.” (If I could get a handle on this (and if it’s true, of course!), it might be resolved for me and render the rest of what I’m saying irrelevant.)

I gave a little description of the treatment of superpositions later in my post, when I described measurements of an electron’s spin. I should note that it is pretty easy to make measurements like this; this description is actually the description of (part of) a classic result called the Stern-Gerlach experiment. It’s experiments like this that convince physicists of the need for superpositions.

Now the problem is, because strongly-quantum-mechanical effects primarily occur far outside of the range of everyday experience, human language is not very well-equipped to describe states like |alive>+|dead>. This I think is where your real problem is. You are trying to describe this state as “both alive and not-alive” and claiming a logical contradiction. But that description is intended to be very loose; it’s not intended as a formal description of the state that you can directly translate into logic in the way you’re trying to do. If you want you can tighten the language to make it clear that there’s no immediate logical contradiction. One way to do this is to eliminate the definitions not-alive<=>dead and not-dead<=>alive, and say that “alive” describes precisely the quantum state |alive>, and “dead” describes precisely the quantum state |dead>. You could then describe the state as “not-alive” (i.e., not the state |alive>) and “not-dead” (i.e., not |dead>) without a logical contradiction. I don’t find this particularly interesting, but I’m more in the shut-up-and-calculate school myself.

What’s more, I don’t see how empirical results can trump principles of logic or reasoning. The whole process of science is built upon certain more or less formal principles of reasoning: “If a theory is confirmed so-and-so many times, we can regard it as true” would be an example. I wholeheartedly agree with this principle, but hopefully we all can see that no experiment has ever, will ever, or could ever be performed to show that it’s a good principle. The scientific process relies quite heavily on the principles of mathematics for instance, principles which themselves are in no way proven by science.

What I’m trying to say in this post is there are certain meta-scientific principles by which science operates that are not themselves provable within science, yet are accepted (NB: I do not take this to mean scientific reasoning is in any way deficient). But why is it that when some results seem to run contrary to a certain principle (non-contradiction), that the impulse in this case is to pitch the principle, not the results?

A full response to these paragraphs would probably be an entire essay on the philosophy of the scientific method; that at least is what my fingers keep trying to type here.

• Why pitch the principle instead of the results? Because that’s the scientific method, as I said earlier. If logic and empirical results disagree, it’s the logic that eventually has to give. Obviously it’s more complicated than this. What usually happens in the most exciting experiments is that a new result appears to contradict an existing physical theory (not “logic”–you still seem to be glossing over the necessary but fallible steps in translation between physical theories and logical statements, which is why you seem to be confused); this is usually because the new experiment takes place outside the parameter regime explored by the previous experiments which were used to “derive” (in an inductive sense, not the logical-proof sense) and confirm that theory. If the new experiment is repeatedly confirmed with enough confidence (something that can’t be done with one-time miracles), then these experiments are used to derive a new theory, and the old theory is now discarded (or considered a special case usable only in restricted circumstances).

• The relation of mathematics and science is much more complicated than you seem to be describing. The Hamster King already did a good job discussing this, so I will stop here for now.

[whc.03grady]

@Candyman74

Which scientific principle, specifically, are you referring to? (Schrodinger’s Cat isn’t a scientific principle).
If you could identify which scientific principle it is that you disagree with, at least we’re all on the same page. And perhaps we can discuss the evidence for that principle, or illustrate how it is successfully used in technology, or how it is used to successfully make predictions.

None. I didn’t say I was disagreeing with any scientific principle. And I realize Schrodinger’s Cat isn’t a scientific principle, it’s a thought experiment.

I’m pointing out what I think may be an instance of a particular branch of science (quantum physics) overstepping the bounds of what science is allowed to make statements about. 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? The particle was unobserved! Science is only supposed to tell us about what IS observed. How can the physicist (who is a scientist, an empiricist) make a claim about a property a particle has during a time when she didn’t look at it?

@Candyman74

Of course [empirical results can trump principles of logic or reasoning]. They must. They have to. Otherwise we’d still believe that the sun revolved around the earth. It was our observations - empirical results - which told us otherwise and contradicted the logic and reasoning of centuries of great thinkers.

The Ptolemaic theory doesn’t entail a contradiction; there’s nothing impossible about it being true. It ISN’T true, yes. But there is a sense in which it could be. Nothing about the discovery that the Earth goes around the Sun (and not the other way 'round) required the revamping or even the serious reconsideration of any principle of reasoning. It did require the revamping and serious reconsideration of certain accepted principles of astronomy (and anthropology, religion, probably others). Big deal. We find out certain of our contingent principles (I should say “principles”) are wrong all the time.

It’s a mistake to think that “logic and reasoning” somehow belong to times or persons, as you seem to be thinking. There’s just no sense in which “If a=b, and b=c, then a=c” was a caveman principle 20,000 years ago and in which it’s a modern human principle now. Mistakes in logic and reasoning may very well belong to times and persons, sure. If a bunch of (or even all) cavemen thought, “If a=b, and b=c, a≠c,” that wouldn’t mean the principles of cavemen reasoning were different than ours, or that reasoning operated differently 20,000 years ago. It would just show that a bunch of cavemen were wrong about transitivity.

@Candyman74

If your observations are at odds with your reasoning, the flaw is much more likely to be in your reasoning than in your observation.

I have no idea on what basis you could make this assertion.

[Telemark]

@whc.03grady

It’s a mistake to think that “logic and reasoning” somehow belong to times or persons, as you seem to be thinking.

It’s a mistake to think that logic as you know it applies to all situations, such as QM where strange things happen.

It’s akin to applying Newtonian logic to a Relativistic situation. How can two objects each traveling towards each other at .9c to a neutral observer appear to approach each other at .99c? It doesn’t make logical sense to in Newtonian terms, but it has been demonstrated to be accurate.

There’s just no sense in which “If a=b, and b=c, then a=c” was a caveman principle 20,000 years ago and in which it’s a modern human principle now.

Yes there is such a sense. It’s called QM, which defies conventional logic.

[The_Hamster_King]

@whc.03grady

If a bunch of (or even all) cavemen thought, “If a=b, and b=c, a≠c,” that wouldn’t mean the principles of cavemen reasoning were different than ours, or that reasoning operated differently 20,000 years ago. It would just show that a bunch of cavemen were wrong about transitivity.

No, it would simply mean they had chosen a mathematics in which the transitive property of equality doesn’t hold. Such a mathematics wouldn’t be much use if they were trying to use it for counting woolly mammoths, but it wouldn’t be “wrong”.

[Cheesesteak]

@Telemark

It’s a mistake to think that logic as you know it applies to all situations, such as QM where strange things happen.

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.

[WarmNPrickly]

@Animastryfe

Please expand on this. What was thought to be logically impossible about C? I assume that by C you mean the speed of light in a vacuum.

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.

[Candyman74]

@whc.03grady

None. I didn’t say I was disagreeing with any scientific principle. And I realize Schrodinger’s Cat isn’t a scientific principle, it’s a thought experiment.

I’m pointing out what I think may be an instance of a particular branch of science (quantum physics) overstepping the bounds of what science is allowed to make statements about. 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? The particle was unobserved! Science is only supposed to tell us about what IS observed. How can the physicist (who is a scientist, an empiricist) make a claim about a property a particle has during a time when she didn’t look at it?

Huh? You can observe the properties of a particle. You just can’t accurately determine both its position and velocity at the same time.

I have no idea on what basis you could make this assertion.

Clearly.
I’m afraid the whole subject of the scientific method is too much for me to want to get into a long debate about. I’ll leave it to others; suffice it to say that you are misunderstanding some fairly fundamental concepts. But it’s too much for me to want to engage in because I know how these threads go.

[Leo_Bloom]

@whc.03grady

I don’t see how empirical results can trump principles of logic or reasoning. The whole process of science is built upon certain more or less formal principles of reasoning: “If a theory is confirmed so-and-so many times, we can regard it as true” would be an example. I wholeheartedly agree with this principle, but hopefully we all can see that no experiment has ever, will ever, or could ever be performed to show that it’s a good principle. The scientific process relies quite heavily on the principles of mathematics for instance, principles which themselves are in no way proven by science.

That mathematics and proof of its correctness needs science for validation is backwards, I believe, but that is an enormous and different field of inquiry.

[Bold mine]
Experiments are what are important. If, for example, after four million times of looking sideways at a Hereford cow, a principle is established that Herefords are spotted. But along comes someone who figures out that 1) there may be another side to the cow, and 2) tries to get a way to confirm this, checking 1) against 2), repeatedly.

Then maybe the former principle begins to totter.

(Isn’t there some joke about this example? Or one about the Umpire, the someone, and the someone judging reality?)

[whc.03grady]

@Candyman74

I have no idea on what basis you could make this assertion.

Clearly.
I’m afraid the whole subject of the scientific method is too much for me to want to get into a long debate about. I’ll leave it to others; suffice it to say that you are misunderstanding some fairly fundamental concepts. But it’s too much for me to want to engage in because I know how these threads go.

I’m sorry if you think I’m trying to drag you (or anyone) into a debate on the pitfalls of the scientific method (if there are any), or anything like that. Myself, I don’t know how such threads usually go but if you’re worried that I’m looking for some point at which I can say “a-HA! Science is fundamentally flawed, the Bible is the literal truth, evolution sucks”, trust me, I’m not going there (it would be pretty weird if I did, as a dyed-in-the-wool atheist). But like I said, I don’t know if that’s how these threads usually pan out anyway, that’s just my guess. If I were to debate someone on the subject of the scientific method, I assure you, I’d keep it on the level (which isn’t to say I’d just unquestioningly eat up anything you’d try to feed me).

I also appreciate the responses you and others have given of examples of revolutions in science, but those kinds of shifts in thinking aren’t what I see to be happening in the situation being discussed (quantum physics). This situation is different from any other revolution in science I can think of–Copernican, Newtonian, Darwinian, Einsteinian–in that it’s not some contingent principle that’s being overturned, it’s something much deeper.

If anyone who’s made it this far doesn’t understand just how utterly, completely, mind-blowingly, dauntingly different the claims of quantum physics are from the claims of any of these others (respectively and in short, “The Earth goes around the Sun,” “An object at rest tends to stay at rest, etc.,” “Human beings, like all biota, are descended and differentiated from antecedent forms by the mechanism of natural selection,” “Light is the speed limit of the universe”), then I thank you for your time.

I don’t take myself to be smarter than most of you and certainly not smarter than the average quantum physicist. But I have a degree (and some graduate study but no post-graduate degree in) philosophy (analytic philosophy, not the wishy-washy, beret-wearing, coffeehouse kind), so pardon me but I’m not inclined, generally, to take advice to “just trust what the scientists are saying” lightly, at least for these types of results.

The assertions of quantum physics don’t just sound weird. That’s the understatement of the year. To be told that a thing can both be something and not be something, at the same time, well, that’s a lot (a LOT) weirder than being told the Earth goes around the Sun and not vice versa.

Now if it’s like Omphaloskeptic says and I’m seeing the claim of a contradiction where there isn’t one, then that’s something I’d like to know because I like to know when I’m wrong. (I’ve read and reread your posts, Omphaloskeptic; thank you.) The Hamster King has made some enlightening comments as well (though none I haven’t heard before, no offense; it’s just that Phil Sci was a few years ago), and perhaps point the way to where I should focus my energy; maybe at base I’m struggling with certain assumptions of the scientific method, and is expressed as a misunderstanding of the results of quantum physics.

Anyway.

[Giraffe]

@DrDeth

And of course, the thought experiment IS ridiculous, as the cat is a observer.

The cat is not the observer, in the wavefunction-collapsing sense. The cyanide capsule is the observer, as it couples to the radioactive decay in a way that distinguishes between the decayed and non-decayed states. The cat is merely an unfortunate bystander.

And Schrodinger’s Cat pisses me off. Because it’s well known, way too many people believe it’s true. It’s not. As others have pointed out, it’s just a complicated way of looking at randomness. Replace the cat and cyanide with a pair of dice: are dice in a superposition of all possible rolls before you open the box? No. Quantum observation is not about knowledge, it’s about interaction: if you interact significantly enough with a quantum system in a superposition, that forces a collapse into a single state. It doesn’t matter if a person or a cat or a cow learns the result of the interaction, any more than trees falling in the woods fail to make sound if people aren’t around. And it doesn’t scale up.

[clairobscur]

@whc.03grady

I didn’t take it as rude.

I think I see what you’re saying. So if the mathematician shows that 1+1=3, and that result is confirmed over and over again, then we’re supposed to accept the absurd (or “absurd”) result and maybe give her a prize.

But there are a number of perfectly absurd theories in physics that have been verified by experimentation. The particle going through two slits at the same time that a previous poster mentioned, for instance.

So, it’s already a given that our perception of what is absurd or logical just isn’t reliable in physics. And, as a result, there’s no reason to scrutinize more (or less) a theory because it contradicts common sense.

[clairobscur]

@Leo_Bloom

(Isn’t there some joke about this example? Or one about the Umpire, the someone, and the someone judging reality?)

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)