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Pooh-Bah
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Would you say the following was a plausible interpretation of Schroedinger's famous analogy:
The truth condition of an untested proposition is such that the argument can be true if and only if it remains untested. If, then, one should test the proposition, it will necessarily be false, its truth value being otherwise indeterminate.
If so, how would one express this as an argument in logical positivistic terms, that is, with respect to a physical state of being and not merely to an argument?
Thanks,
IP
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Are you equating the argument as being that the cat is both dead and alive?
I've always thought that all Schrödinger's cat showed us is that we can't draw conclusions from ignorance.
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If you don't already have a headache like mine, try reading this translation of the otiginal paper. I'm sure it will give you one. http://www.qedcorp.com/pcr/pcr/qcat.html
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try reading this translation
Not tonight dear, I have a headache.
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okay, here's one layperson's translation:
You put a cat in a box. Then you have poison that can be triggered by a quantum event-perhaps a half-silvered mirror that you send an electron through. The electron has a fifty-fifty chance of actually going through the mirror. If it goes through, it triggers the poison. So there's a 50% chance that the cat is dead, and a 50% chance that the cat is alive. But according to quantum theory, until the observation is made, the electron both did and didn't go through the mirror, and the cat is therefore both dead and alive. Schrödinger said that according to quantum theory, until a conscious observer opens the box and looks, the cat is both dead and alive.
Schrödinger's point was that the conscious observer interpretation was absurd.
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and Heisenberg said that when you opened the door you changed the outcome anyway, so why bother looking... 
formerly known as etaoin...
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Pooh-Bah
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No. I'm suggesting that the proposition that the cat is alive is by definition untestable and that its truth value is therefore indeterminate. This is in distinction to the proposition that "the cat observed is dead" is unambiguously true. I am not suggesting that S's cat says that "the cat is at once both alive and dead" is true.
I think Schroedinger's cat is a demonstration, by analogy, of the uncertainty principle of quantum mechanics. But although it seems to deal with the conditions of a physical fact, what it really does is propose a truth condition for a proposition, i.e., that "the cat is alive." In this, it is distinguished from the uncertainty principle which deals with actual observation of actual phenomena in terms of the definitive pairs of qualities of those phenomena: position and speed. Unlike the viability/lack of viability of the cat, however, the position and speed of an electron are not expressions of a logical argument; they are properties of a physical phenomenon. If I am right, S's cat is only meant to illustrate the uncertainty principle by means of a thought experiment that is only partially analogous to it.
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hehe. got ya' by 5 seconds...
formerly known as etaoin...
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Pooh-Bah
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Thanks, tsuwm.
Although your clarification does make my project a bit more difficult.
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In truth, the cat is just too big to validate the analogy.
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Pooh-Bah
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And thanks, wwh, for the link.
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the cat is just too big
Not to mention observing the whole time (at least whilst still alive).
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Did Schrödinger's cat have nine lives?
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How stupid. The silly word-a-gram "Schroeders Cat" is a meaningless construction that only has function in a child's game. Forgive me. I try my best to be polite.
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Dear Milum: Sorry about the nine lives bit.
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You know, I may or may not get involved in this discussion.
Actually, the preceding sentence is to examine the absurdity of the construction. "I may or may not" makes me do a slow burn whenever someone uses it. An old boss of mine used to make me even crazier by putting hand quotes around the phrase whenever he said it, and he said it pretty often.
It was just over eight years ago that I went to my last office Christmas party, and this man's performance at that one was the reason for my forgoing these annual events, even after he retired. This was a very small gorup, perhaps ten people, so we decided to have a Christmas lunch at the Rattlesnake Club in Denver, a pretty expensive and wonderful place.
When we got there, Bill was in his cups, and we seated ourselves around the table with some trepidation. The waiter came out and Bill ordered a bottle of wine. The waiter got the bottle, opened it, and poured a small glass for everyone at the table.
Bill stood up, grabbed the waiter by the tie and pushed him against the wall. "Listen, you little motherf*****r, that was for me. Bring me another bottle right now."
The silence was overwhelming as we all got up and walked out.
TEd
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Irregardless of whether or not I [bucky quotes]may or may not[/bucky quotes] get into this conversation or not...
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Pooh-Bah
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Well the nine lives quip gave me a good laugh...
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> Schrödinger's point was that the conscious observer interpretation was absurd
This sounds right to me. And although poor ol' Heisenberg may have been much maligned for his trying to include such insignificant details of the universe as life and consciousness into a model of the world at least he had the gumption to try. The idea of completely consensual reality is no more absurd than this cat in the box.
Far more profound than any subjectivity, relativity or chaos theory are the ideas of the little-known German, Högel I'd say. He proved mathematically (some which way) that any expressions for a system created or perceived 'present' cannot be defined within its own terms or borders. This came coupled with the uncomfortable realization that 2+2 does not equal 4 but that it is merely a strong tendency.
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isn't that Kurt Gödel? as in Gödel, Escher, and Bach?
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Kurt Gödel
I don't think that Gödel proved that 2+2 <> 4. He proved that any system sufficiently complex could not be both complete and consistent. It used to be believed (as per the Shrödinger article) that if we knew the the initial conditions of a system and we knew all of the rules determining the system, that we could then perfectly predict everything about the system at any moment in the future. (This assumes of course that the system was deterministic.) We believed that the universe was understandable, that it was deterministic, that it was causal, that it was logical. But ... weird stuff was happening ... things that contradicted basic assumptions - some of them assumptions so basic that few, if any, had ever thought to question them.
Gauss, Bolyai, et. al., showed that despite supposed proof by Kant to the contary, that one could develop a consistent geometry replacing Euclid's fifth postulate with something inconsistent with it.
Cantor showed that not all infinities are equal, some infinities are bigger than others.
Michelson and Morley show that there is no ether ... but if there is no ether, through what do light waves travel? How can you have a wave without a medium?
Russell and Whitehead spent years in a thought-provoking, but failed attempt at showing that mathematics could be derived from logic.
A patent clerk publishes a paper in Annalen der Physik that in a very few paragraphs (and if I recall correctly not a single reference) questions our ideas about simultaneity and absoluteness. The speed of light does not depend on the speed of the source or the reciever. It's absolute (in a vacuum). [A common layman's MIS-understanding is that Einstein said "everthing is relative."] In any case, what he actually proposes violates our classical assumption that velocity vectors are additive.
Said clerk had previously published a paper in same journal explaining that in addition to obvious wave properties, light also exhibits some particle properties (waited for De Broglie, Germer, et al to 'reconcile').
Heisenberg states remarkable conclusion that we can't perfectly know position AND momentum of a particle, not because we have bad eyes, or faulty equipment, but because of a fundamental aspect of nature - when we look at something (measure it), we change it. We can know these things, but only within the constraints of the uncertainty relation.
Bohr and others advance the copenhagen interpretation (which I don't understand and I don't even remember what I read about it) and Schrodinger graciously volunteers his cat for an experiment to show the aburdity of this view.
While the feline is in the box, she's out of the bag. Mystics the world over use this knowledge as final proof of what they've always believed - that there is no objective reality. (No idea how they get there from here, and I don't understand this stuff well enough to argue the point - but I have a strong suspicion that these guys are misinterpreting things.)
Godel develops his incompleteness theorem. Even if you knew all the rules of a sufficiently complex system, you STILL couldn't prove that all the true statements are true. If you could magically find another true statement and at it to the list of axioms, you still would YET be true statements that couldn't be proved to be so.
It's not easy for me to recognize one thing or person that is more important than the others in the demolition of the classical view (although I, too, have a soft place for Godel.) Each of these is a pretty startling development - even now.
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> isn't that Kurt Gödel? as in Gödel, Escher, and Bach?
Spell dyslexia for me there, eation. [sic]
Thanks for the explanation FallibleFiend. I didn't mean to suggest that Kurt proved that 2+2 didn't equal 4, more that, as far as I know, maths was coming to recognize this possibility (or truth?) at about this time.
Can you, at the risk of p-ing off InselPeter, also explain these new theories regarding the speed of light as not being the 'speed limit' for the universe?
The orignality of any idea is directly proportionate to the knowledge of the audience.
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"Can you, at the risk of p-ing off InselPeter, also explain these new theories regarding the speed of light as not being the 'speed limit' for the universe?"
I'm afraid not. It's way outside my area of expertise - in fact, all of this is (well, except for the Goedel stuff, which is almost comprehensible).
I work with a crapload of PhDs in various fields, though, and I sent a query to one of my buds several months back asking about this and recieved no reply. He got his physics degree from BU about a million years ago, so he's kinduva curmudgeony, old fart, and usually busy, but sometimes he'll give me the time of day. (Actually, he's a really nice - crotchety - guy, but he's pretty busy.)
I recall an article I read decades ago about a model of tachyon, tardyon, and photon universes. Tachyon is FTL, Tardyon is STL (slower than light). Each universe is tardyon wrt itself, but tachyon with respect to the other universe. After I read the article (smithsonian? SciAm?), I wasn't sure whether this was just a curiosity derived from a mathematical excursion, or something someone was seriously proposing. I pretty much forgot about it till a few months ago when I read about the experiment where the guys had apparently achieved FTL communication - a clear violation (FTL is not impossible, according to Martin Gardner, it's FTL with transfer of information that's impossible). However, I don't think the experimenters themselves believe they (Wang, et. al.) achieved FTL communication. If I recall, they were very skeptical and seemed to indicate it was some sort of artifact of their experimental design. Really, I didn't understand this very well when I read it, and my memory sucks, so it's anybody's guess what they really meant. If you look for it, you might be able to find it on the web. Maybe you can make more sense of it than I could. (I can't find my old email to my friend on it.)
Just as an aside (and not as a jab or anything) - aren't you at university? That's a great time to make friends with people all over campus. People dog the "old boy network" and it does have a lot of potential for abuse, but it's also an extremely valuable thing - not just professionally, but on a personal level. Not a lecture or anything. Not even advice, really. Just a stating my own experience.
good luck,
k
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Pooh-Bah
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The final arguments:
Reader Query of Cecil, the doyen of a scientific newsgroup I've long since lost track of:
Cecil, you're my final hope
Of finding out the true Straight Dope
For I have been reading of Schrodinger's cat
But none of my cats are at all like that.
This unusual animal (so it is said)
Is simultaneously live and dead!
What I don't understand is just why he
Can't be one or the other, unquestionably.
My future now hangs in between eigenstates.
In one I'm enlightened, the other I ain't.
If you understand, Cecil, then show me the way
And rescue my psyche from quantum decay.
But if this queer thing has perplexed even you,
Then I will and won't see you in Schrodinger's zoo.
-Randy F., Chicago
Cecil's Reply:
Schrodinger, Erwin! Professor of Physics!
Wrote daring equations! Confounded his critics!
(Not bad, eh? Don't worry. This part of the verse
Starts off pretty good, but it gets a lot worse.)
Win saw that the theory that Newton'd invented
By Einstein's discov'ries had been badly dented.
What now? wailed his colleagues. Said Erwin, "Don't panic,
No grease monkey I, but a quantum mechanic.
Consider electrons. Now, these teeny articles
Are sometimes like waves, and then sometimes like particles.
If that's not confusing, the nuclear dance
Of electrons and suchlike is governed by chance!
No sweat, though - my theory permits us to judge
Where some of 'em is and the rest of 'em was."
Not everyone bought this. It threatened to wreck
The comforting linkage of cause and effect.
E'en Einstein had doubts, and so Schrodinger tried
To tell him what quantum mechanics implied.
Said Win to Al, "Brother, suppose we've a cat,
And inside a tube we have put that cat at -
Along with a solitaire deck and some Fritos,
A bottle of Night Train, a couple of mosquitoes
(Or something else rhyming) and, oh, if you got 'em,
One vial prussic acid, one decaying ottom
Or atom - whatever - but when it emits,
A trigger device blasts the vial to bits
Which snuffs our poor kitty. The odds of this crime
Are 50 to 50 per hour each time.
The cylinder's sealed. The hour's passed away. Is
Our pussy still purring - or pushing up daisies?
Now, you'd say the cat either lives or it don't
But quantum mechanics is stubborn and won't.
Statistically speaking, the cat (goes the joke),
Is half a cat breathing and half a cat croaked.
To some this may seem a ridiculous split,
But quantum mechanics must answer, 'Tough shit.
We may not know much, but one thing's fo,sho':
There's things in the cosmos that we cannot know.
Shine light on electrons - you'll cause them to swerve.
The act of observing disturbs the observed -
Which ruins the test. But then if there's no testing
To see if a particle's moving or resting
Why try to conjecture? Pure useless endeavor!
We know probability - certainty, never.'
The effect of this notion? I very much fear
'Twill make doubtful all things that were formerly clear.
Till soon the cat doctors will say in reports,
'We've just flipped a coin and we've learned he's a corpse.'"
So said Herr Erwin. Quoth Albert, "You're nuts.
God doesn't play dice with the universe, putz.
I'll prove it!" he said, and the Lord knows he tried -
In vain - until fin'ly he more or less died.
Win spoke at the funeral: "Listen, dear friends,
Sweet Al was my buddy. I must make amends.
Though he doubted my theory, I'll say of this saint:
Ten-to-one he's in heaven - but five bucks says he ain't."
- Pfranz
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haha! that's terrific. thanks for sharing.
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The following has been circulating over the net for a couple decades at least.
UNIFIED FIELD THEORY by TIM JOSEPH
In the beginning there was Aristotle,
At objects at rest tended to remain at rest,
And objects in motion tended to come to rest,
And soon everything was at rest,
And God saw that it was boring.
Then God created Newton,
And objects at rest tended to remain at rest,
But objects in motion tended to remain in motion,
And energy was conserved and momentum was conserved
and matter was conserved,
And God saw that it was conservative.
Then God created Einstein,
And everything was relative,
And fast things became short,
And straight things became curved,
And the universe was filled with inertial frames,
And God saw that it was relatively general, but some
of it was especially relative.
Then God created Bohr,
And there was the principle,
And the principle was quantum,
And all things were quantified,
But some things were still relative,
And God saw that it was confusing.
Then God was going to create Ferguson,
And Ferguson would have unified,
And he would have fielded a theory,
And all would have been one,
But it was the seventh day,
And God rested,
And objects at rest tend to remain at rest.
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UNIFIED FIELD THEORY by TIM JOSEPH
So nice to see this actually credited. Tim Joseph is the Chairman of the Tompkins County Board of Representatives, the group whose twice-monthly meetings I do camera for. There are many copies floating around the web uncredited. He'll be interested in seeing that his spelling of Furgeson has been "corrected". I asked him about that once and he had some reason for the spelling he used but I forget what it was. Looks like there's two days missing.
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UNIFIED FIELD THEORY by TIM JOSEPH
Crediting was an accident. The site I snagged it from happened to include it.
First time I ever saw it was on crinkled old paper (that green and white striped stuff) hanging up in the Engineering Computer Lab (ECL) in the basement of Speed School (U of Louisville) - just about two decades ago. It was hanging next to the 6 phases of an engineering project (1. enthusiasm, 2. disillusionment, 3. Panic, 4. search for the guilty, 5. punish the innocent, 6. praise and honors for the non-participants - no attribution because I don't know where it originated).
I remember this was some of the first stuff I ever saw just hanging up on a wall at college and thought college guys must be the smartest people in the world to think such clever thoughts.
k
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Crediting was an accident. The site I snagged it from happened to include it.
Huh?
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Huh?It's all over the place. Apparently first publication was in Analog about 20 yrs ago. Google unified furgeson. There's even a German transltion out there. Credited. http://www.borsche.de/borsche/inhalte/furge.htmThe Zeit link at the bottom of the page seems to be broken.
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