It takes a perfectly reasonable situation (a wavefunction with a 50% probability of being in either of two states) and attempts (not very well, really, considering how brilliant Schroedinger was generally) to relate it to “the real world,” causing untold confusion to countless people who are desperately trying to make sense of this.
I have no idea what point Schroedinger was actually trying to illustrate with the cat story. Knowing his own biases, I expect it’s an attempt at analogy, though if it were called “Einstein’s Cat” I’d suspect that he had used the same story to illustrate how ridiculous the idea was. The actual experiment as described is a bogus example, since triggering the detector is an “observation” even if no human ever looks at the results.
Badenov’s Cat is basically the same story without the quantum mechanical trappings. See, either there’s a live cat (50% chance) which is worth $1000, or a dead cat (50% chance) which is worth approximately squat. Expectation value: $500. In other words, if you did this a million times, you could reasonably expect to end up with pretty close to $500,000,000 worth of cats. You might have the world’s worst run of bad luck and every one of those million cats would die, or you might have the luck of the Irish and every one would be alive. However, half-and-half is a much more likely outcome.
Or, to put “expectation value” another way: if you can buy a “cat future” (that is, you own the cat when the safe opens) for less than $500, it’s a good deal for you. If you pay more than that, it’s a good deal for the other guy. $500 is perfectly fair to both of you.
Yeah, torq pretty much lays out what I was getting at. If someone offers to sell you the contents of the vault for $499.95 (before the third day), take the deal. If they offer it for $501, tell them no. It’s not that important in a single instance, it’s just smart as a policy.
I think Schrodinger picked life-and-death as a way of illustrating how this principle can be applied to some pretty weird stuff. If you take these principles literally, the cat can be half-dead / half-alive, women can be sort-of-pregnant, and the expected value of buying a $2 lottery ticket can be negative $1.50.
Whether Schrodinger was saying this kind of thinking is worthless, or whether he’s just illustrating the pitfalls, I don’t know. Maybe he was just having a good laugh.
My current wild guess is, he was saying: don’t worry too much about quantum mechanics working in a tangible, macroscopic way. It’s too weird for our overgrown brains to understand (notice, saying our brains are too puny to understand doesn’t make sense, our scale is too large for this, not too small). So keep your quantum analyses in the proper scale. Metaphors and models are limited … curiosity half-killed the cat.
My problem is not the metaphors, it’s figuring out what they are applied to. The whole thing stems from an inability to know both the location and speed of an electron in the orbital of an atom, is that right? What would be the point of that? I’m not saying it’s useless, I’m just wondering what application this stuff has, or if it’s just theory.
Sorry, I know this is not exactly germane, but I couldn’t help myself.
How to Catch Lions in the Sahara Desert
The method of inversive geometry.
We place a spherical cage in the desert, enter it, and lock it. We perform an inversion with respect to the cage. The lion is then on the interior of the cage, and we are outside.
A topological method.
We observe that a lion has at least the connectivity of the torus. We transport the desert into four-space. It is then possible to carry out such a deformation that the lion can be returned to three-space in a knotted condition. He is then helpless.
The thermodynamical method.
We construct a semi-permeable membrane, permeable to everything but lions, and sweep it across the desert.
The Schrodinger method.
At any given moment there is a lion in the cage. Sit down and wait.
-excerpts from the American Institute of Useless Research
I think I’m following some of this, but the cat problem seems to be a coin toss thing, nothing to do with quantum mechanics. If a person flips a dollar coin and covers it and says, by the accounting idea above, “if you guess right you can have it, how much will you give me to try?” Then the best answer is $.50 . But if he says, “what is it, heads or tails?” Then I’m not buying the idea that it is both.
Oh my! Now I feel so inadequate near
All those talking in prose in this thread over here.
See, the letter addressed to dear Cecil from one
Of us Teeming Millions tried to have some wee fun
By talking of this famous half-living cat
In dactylic tetrameter – rhyme! Believe that?
But our Unca Cecil, he rose to the task
And answered the question the fellow did ask
With a rhyme of his own! And a longer one, too!
Like A Visit from Saint Nicholas, it rang true.
Or maybe it sounded more like Dr. Seuss
Except without Seuss’s fake words flopping loose
Like “oobleck” or “hoober-bloob” or “yuzz-matuzz”
Or “frobozzle frobizzle frobnoy snooper snuzz”.
And like always, ol’ Cecil pulled through in the end
With a picture of how quantum physics doth wend
Through its sordid, tumultuous history, full
Of big names like “Einstein”, who on dice did mull
By saying that God doesn’t – can’t – play with them.
(This despite having won a Nobel for Q.M.!)
And I see as I write this the challenge he faced –
“He” being Cecil, with whose words we’re graced –
Because rhyming and making sense at the same time
Would sure be a heck of a lot easier if I got to put a couple of extra syllables into a line.
Burma Shave.
Quick-N-Dirty Aviation: Trading altitude for airspeed since 1992.
At the quantum level, a particle exists as a probablity wave until it interacts with the non-quantum level (i.e., the macro world, an observer).
As a probability wave, all possible states that the particle can be in all exist – at the same time!
This is where the paradox comes in. At the macro level objects don’t behave that way. A cat, for instance, in a house can theoretically be anywhere in the house. But the cat isn’t everywhere in the house with varying degrees of possibility. The cat always has a definite place and momentum.
And yet, quantum level particles exist everywhere at once at varying degrees of possibility until they interact with the macro world and are ‘fixed’ in place (or momentum).
S’s cat paradox tries to take the probability wave of a quantum particle and make it apply to the macro world in an attempt to make us think about how and why quantum state particles lose their probablility wave in the first place when interacting with the macro world. And it makes us question how and why the macro world, which is made up of quantum particles, do not behave like quantum particles but have a definite place and momentum.
The S. Cat Paradox is not an epistemological problem, it is a metaphysical one. Oops, I’ve stopped being ‘pop’.
The point of Schroedinger’s experiment is that it is a metaphor for the uncertainty of quantum physics. Most events in the universe can, at least theoretically, be predicted by studying the events which preceded them. For example, if you know the mass of a hammer and the earth and how high you are holding the hammer, you can easily predict how much time it will take the hammer to strike the earth if you release it. But there are events that occur at the quantum level which are totally unpredictable, even in theory. Schroedinger designed his experiment to illustrate for people who couldn’t follow quantum physics how it is possible to have an event where you know all the facts that created a situation but have no predictable outcome.
It doesn’t matter untill you open the box, at which time you know. Then you should find peace by accepting whichever state the cat is in. The good thing is, if it’s dead, it’s already in a box. Maybe Schroedinger is why people started burying their pets in boxes in the back yard. See, I knew there was an answer to something in there…
Thanks, moriah, your explanation made the most sense to me – precisely, I suspect, because you took the cat out of it. But now I have another question: if a particle wave has the potential to be either one thing or another (alive or dead, to go back to the analogy) at the time it interacts with the macro-world, why does that mean it is both prior to that? Couldn’t it just as reasonably be said that it is neither – that it is, in fact, merely a potentiality until the interaction occurs?
I think there is still confusion here. Some people think that the ‘observer’ in question must be a human. A cat (or a quarter) will work fine. If this experiment were actually done, the cat would either be alive or dead. Whether people know the answer is irrelevant to the cat.
Exactly, Cooper; that’s one of the reasons I hate the story.
Anyhow:
jodih, if you really want to understand this stuff, go to a library and find the “Feynman Lectures on Physics, Volume III.” Start with Chapter 1 and read through Chapter 3. It explains the same concept, with nary a cat in sight, though he does discuss trees falling in forests.
Schrodinger died in 1961, and by that time he had already had the cat in a box for years. It is now 38 years later. I am sure the damn cat is dead by now, quantum mechanics notwithstanding.
I think maybe the difficulty is accepting that, prior to the ‘collapse of the wavefunction’ ie the determination of the state of whatever you’ve observed, the object, be it a cat or whatever, exists as a combination of all possible states (with varying probabilities obviously)…it’s just something which doesn’t tie with the macroscopic world we occupy, but has to be accepted. That’s how I get round this type of stuff. Accept it. This wasn’t helpful was it.
I would go get a textbook, but then I wouldn’t be able to resist marching around going “Look, I’m reading physics! For fun!” People who know me would never believe it and would laugh at me; people who don’t know me would rightly smack me for pretentiousness. Do they publish “Physics for Dummies”? That’s what I need.
Well, whenever I wanted to know about this type of thing, i’d either go to an old standard undergrad text, ‘Quantum mechanics’ by L. Schiff, I think, or a really cool little book called “The Quantum World” By the Rev. Dr. J.C. Polkinghorne…it’s really readable and fun. Another is called “Relativity for the Layman” but i’ve forgotten the name of the author. Oh, and unless your maths is awesome, don’t bother with Schiff.
