I stole that 
The best explanation I can give for quantum superposition:
Consider a representation where “alive” is a vertical line, and “dead” is a horizontal line. In such a representation, the cat’s state may be described as a diagonal line. And yes, there are two different diagonal lines you could use: / or . Those are two different superposed states, and which one of the two the cat is in would depend on the details of how the experiment is constructed, what sort of unstable particle you had decaying, etc.
The one things I’ve never understood is, what is the definition of observing? How does studying a particle (or its effects) affect that particle? Is there an interaction going on, on a subatomic level when one observes a particle?
Mathematically an observation is is made with a quantum mechanical operator. For instance to measure momentum the operator is (hbar/i)(d/dx), but this doesn’t answer your question.
The real answer is nobody has the foggiest idea. How do you perform a physical measurement on something when all you have to work with is a wavefunction that doesn’t carry energy and therefore isn’t even real?
Irish Physicist John Steward Bell, a vegetarian and animal lover famous for the eponymous Bell’s Inequality, a response to the Einstein_Podolsky-Rosen Paradox, changed the experiment such that the decay of the isotope released a container of food, such that the cat, instead of being alive or dead, is now fed or unfed. Lord love the Irish.
As for the experiment itself, it was indeed intended to highlight the absurdity of quantum mechanics. The reason we aren’t normally bothered by the apparent statistical nature of QM is because of a behavior called decoherence; in essence, once you clump enough particles together into a macroscopic object the variations average out and the statistical behavior isn’t apparent on any perceivable scale. For instance, while a single electron may be here one minute and across the state in the next, the sum total of all of the electrons in a baseball are exactly where they need to be in order to maintain the electrochemical bonds that keep the atoms comprising the baseball together. That a stray electron out of tens of billions in the ball might disappear is not only of no significant consequence but in fact completely immeasurable; its loss cannot be detected by inspecting or weighing the ball as the variation is too slight to appear above any normal variations from the thermal energy in the ball.
Schrödinger, unhappy (as many were) with the statistical nature of fundamental behavior as described by QM, found this to be wrong-headed and set out to design a Gedankenexperiment that caused some macro system (the poison and cat) to be influenced by a single quantum event (the isotope decay). This breaks through the barrier of decoherence and thus, would demonstrate that behavior is or is not stochastic as described by QM. The problem, of course, is that the experiment is impossible; even if you could physically execute the experiment, you still wouldn’t be able to perceive (by sight, sound, x-ray, clairvoyance , or any other means) the state of the cat without causing the cat-in-box system to collapse to a discrete state. However, the idea that objects behind the door are floating in superposition until the door is opened is so contrary to normal experience that it makes the Copenhagen Interpretation seem impossible.
However, the Schrödinger’s Cat experiment doesn’t address the fact that we can, in fact, see quantum behavior on an everyday scale, and particularly in what is popularly known as the Double Slit (or Two-Slit) experiment. This experiment is run on a macro scale in high school physics labs as an example of wave interference; that is, when a wave encounters two slits (of a given width and separation) the resulting energy of the wave that is now split in half will create interference patterns. This is because waves are distributed energy transmitted in some kind of fluid continuum medium, and perfectly acceptable by classic physics. However, when we deal with fundamental particles like electrons or photons, we expect them to act discretely, as indicated by photoelectric effect, which showed that photons and electrons have discrete energy levels relating to their frequency. So we expect that a particle will either go through one slit or the other, and in fact, if you put some kind of detector right before the slit you’ll see it go through one slit or the other 50% of the time each. However, if you don’t watch the particle before it goes through the slit it makes an interference pattern with itself that looks just like a wave. In other words, it displays wave-like and distinctly un-particle-like behavior when not observed, but acts like a particle and not a wave when you’re paying attention to it!* Even better, it does this retroactively; that is, if you give the particle two widely separated paths between which there could be no interaction and only observe it at the end of the paths just before it goes through a slit, it still picks one or the other while observed, and is distributed when it isn’t.
In the immortal words of Keanu Reeves, “Whoa!”
This has led to a number of interpretations, including (as alluded to in previous posts) the Consciousness Causes Collapse (CCC) Interpretation, in which it is hypothesized that conscious perception causes collapse and that cognition is an inherently quantum function. However, before we all drink the Cool-Aid and jump off the cliff, consider a couple of talking points. One is that by observing the particles in the double-slit experiment, you aren’t just standing back and watching the electron or photon go past; you are actually interacting with it, and this itself will alter its behavior. This is a fundamental problem with any attempt to directly measure or observe behavior on the quantum level using macro-scale instruments. In order to account for the interaction you’d have to evaluation the interaction of all the particles in the target particle/instrument system, which brings you back to decoherence; you don’t know by how much you’ve influenced it versus it influencing you.
Another problem with CCC is the question of, “Who bells the cat?” If we open the box at the same time, does my observation of the cat cause the event to collapse, or does yours, and what happens if I perceive it to be alive and you think it dead? Are our consciousnesses intertwined such that we all cause events the same way, or does some Cosmic Censor come along and fix my memories and perceptions to accord with yours? Eugene Wigner extended the Schrödinger’s Cat experiment to include another layer of abstraction, further highlighting the problem with this interpretation. In it, Wigner has a friend who goes in the room and checks on the state of the cat while Wigner remains outside. The friend comes back out, and because he is now an intertwined part of the cat-poison-box system he is also in superposition until he informs Wigner about the state of the cat. Where is the collapsing wavefront now?
This becomes an inherently solipsistic argument (“the world begins and ends with me,”) that just doesn’t work with two or more truly independent observers. Add to this the fact that there is no indication that cognition (and therefore consciousness) is anything more than a really complex neurochemical phenomena.
The problems arise with other interpretations that have some kind of wavefront hypothesis stemming from an event nucleus. In fact, quantum collapse either has to be occurring continuously and transparently, or there has to be some kind of behind the scenes coordination (either prior agreement or a Bohm-style non-local connectivity) between separated parts of the entire system of the Universe. There are other hypotheses, like the Everett and DeWitt Many-Worlds interpretation, but the sum total is that not one of these interpretations offers any falsifiable method by which to distinguish it from any other, and mathematically they all come to the same result; that the apparent behavior of individual fundamental particles is stochastic, and that when you have a local system of interacting particles of sufficient size the randomness averages out to an essentially discrete system. Physics instructors tend to avoid protracted discussions about interpretations as being futile and generally recommend the “Shut up and calculate,” method when it comes to actually using QM to solve problems.
I would argue that there are underlying but unreadable parameters (called hidden variables) that deterministically define the state of the cat, regardless of who or if anyone observes it. The problem with this, however, is that Bell determined that such variables could not be local; they would have to be stored in the connections between systems that are widely separated and interact in a non-causal manner (i.e. instantaneously between non-local domains). This is in direct contradiction to both relativity and good sense; we don’t want to believe that physical behavior is “random”, especially when every behavior we observe in the macro scale, even chaotic behavior, is subject to cause and effect. However, this interpretation works just as well as any other and is internally consistent (if at odds with relativity) and so it makes me almost as happy as a class of warm Irish whiskey.
I hope this makes everything as clear as a Halliburton accounting statement. If you need further assistance, please push the red button, which will display a sign saying, “Do not push this button again.”
Stranger
The experiment is a failure at what it proposes to do. It’s pretending to be a cat caught between the two quantum states that are in superposition, but in reality it’s reliant on another dichotomy, that of collapsed/non collapsed or coherent/decoherent. What will happen is simply that the cat will stay alive until the Geiger counter blips and then it will die. No one makes a big mystery over whether Geiger counters are in some magical dual state in everyday use, so adding a cat to the equation doesn’t really change anything. Perhaps a better experiment could be devised but this one isn’t meaningful.
I guess it’s comprehensive but it contains some questionable concepts too:
I wish popular science would ban the use of the words ‘observer’ and ‘observation’ from any discussion of QM. Decoherence has nothing at all to do with observation. It has to do with certain interactions, some of which are inevitable when using measuring devices, but these interactions would occur spontaneously without human interaction, and with human interaction that didn’t involve ‘observation’.
This is a real travesty of ignorance, given that passive observation has none of the same affects as observation that relies on interactive measurement. Any physicist that says something like this should be put out to pasture with the ID people.
In the Copenhagen interpretation all you’ve done is added one more step. What does the Geiger Counter do when its not being observed? If you’re observing it then you might as well look inside the box.
Another possibility that’s rarely mentioned is that of so-called objective collapse theories – basically, they say that quantum mechanics just doesn’t carry over to macroscopic objects because the wave function collapses randomly on its own with a likelihood generally tied to some measure of ‘macroscopicness’, total particle number or mass or the like, for instance. This leads to genuine state reduction occurring virtually instantaneously for any reasonably-sized object, prohibiting them from exhibiting quantum superposition. This is not just another interpretation of QM, but an extension requiring genuine new physics, I should add.
The problem with this hypothesis is what comprises a “reasonably-sized object,” i.e. where are the boundaries of said object as a system distinct from everything around it? Something that is a solid continuum has recognizable boundaries from an everyday perspective, but how does an electron “know” that it is part of the object versus just passing by? And with fluid mediums, where is the boundary between being part of a discrete system and just a detached soldier wandering through the forest?
Quantum mechanics is inherently non-intuitive, and most efforts to render it by analogy to a macroscale concept are bound to come apart like a cheap gold watch. It is better to accept QM for being what it is, acknowledge that while we can calculate the mechanics but don’t understand what is going on behind the curtain, and sally forth from that standpoint than to try to force an interpretation that makes sense intuitively but fails to extend the utility of the theory.
Stranger
I have done the experiment myself. In my version of the experiment, if the isotope decays, the door is opened, and the cat can come in or go out. Many a days, my cat goes in and out so often, I am sure that he has somehow quantumly entangled himself with the door and is both in and out at the same time.
Obviously Schrodinger never owned a cat. I’ve directly observed my cat in the afternoon many a day and could never tell if he was in fact dead or alive.
Great post. I have wrestled with this fairly long and hard for an amateur who flunked out of calculus, and there’s a book I highly recommend on the subject called Time’s Arrow and Archimedes’ Point by an Australian philosopher/physicist named Huw Price.
Price’s argument is sufficiently compelling that once I’d (sort of) understood it, it kind of ruined the fun of the two-slits experiment for me, the way learning how a cool magic trick is done deflates one’s sense of wonder at it.
I’m too lazy to mangle the details here, but basically Price makes a strong case that the Second Law of Thermodynamics is an artefact of the universe being the way it is, rather than an immutable physical law like, say, Newton’s laws of motion.
Which basically means that we only have time, as we know it, as a consequence of the universe’s recovery from a state of unnaturally low entropy to its “customary” state of high entropy-- in other words, one-way time is something only seen in a post-Big-Bang type of situation. It isn’t “real.”
Once time becomes a contingent rather than a necessary feature of the universe, a lot of what we assume about causality becomes suspect, and the two-slits experiment starts to make sense. (I realize I haven’t explained how-- I’m barely smart enough to feel like I almost get this for short bursts; I’m definitely not sharp enough to explain it.)
Another nice thing about Price’s book is that it resolves a lot of quantum weirdness without resorting to the loony anthropocentric hand-waving of some of Copenhagen’s more extreme descendents. (So-called documentary “What the Bleep Do We Know,” I’m looking at you.)
To put the above in a more epigrammatic form:
The Second Law of Thermodynamics sure does command a lot of respect for a principle that implies that the universe as we know it shouldn’t exist.
I’m pretty sure observation doesn’t have any affect at all on the Geiger counter. Messing around with the radioisotope might cause it to decay quicker, but if you leave it alone it will inevitably decay without our help.
From my understanding (I’m not a scientist), at the point in time that the atom decays, a particle is created or released. That is a natural “observation”. Naturally, any time before that, the Geiger counter has not observed anything. If there were another simple way to probe the atom before it decays, we would see it in the un-decayed position (a human caused observation). If a random stray photon hits it, that would be a natural observation. At all of these points it would act as the un-decayed atom would act. I imagine that some of these interactions could affect the likelihood of decay, but lets ignore that for now.
During all of this time, at each instant (say at every plank time interval?), there is a 1 in X chance that it could decay. At this point it is a wave that is somewhere between “stay in this state” and “decay”. When you look at it through some other minimally-intrusive measuring device, if it does decay before you observe, you will observe “decayed” otherwise you will observe “not decayed”. This is a relatively simple uncertain scenario: at some statistically defined point it will decay, and over this time it will be in an uncertain state that when observed will appear to be “un-decayed” until it does decay.
I imagine the probability wave to be chaotic and very variable in amplitude. When that wave reaches a high enough energy level, the decay happens. The wave may be an expression of the number/energy of virtual particles in the area. For example, suppose the decay needs a certain energy level to happen, and there are a statistically defined number of virtual particles in the region that contribute energy to make the decay happen. The number of virtual particles there at any given moment goes up and down by huge amounts, and once in a while there will be enough of them to push the atom into decay. The rate that that happens defines the half life of the atom.
In the case of the photon going through the double slits, I imagine the photon to be a spherical field that holds the energy of the photon. When it gets to the un-observed slits, part of this sphere goes through one slit, and part through the other, possibly fanning out through the process. This is when entanglement happens. Then when the leading edge of this fanned out wave/energy field hits the wall it is observed. Then the entangled energy field that represents the probability of where the photon is collapses and the interference pattern emerges. If there is a sensor that senses the photon near enough to the slits, it causes the entanglement to collapse at that point, before it has spread far enough to show the interference.
Another way to look at a photon is as a swarm of virtual particles, with the density of the particles following a bell shaped curve from high at the center of the field, to very low far from the center. So, when this swarm of virtual particles runs into something that qualifies as an observation, one of them becomes the “real” photon for this interaction. Assuming the photon carries all of its energy away in an unaltered form, it goes back to being a swarm of virtual particles.
In the double slit, this field gets spread out into a fan that eventually hits the wall, and then collapses into one of those virtual particles, and that point on the wall is where all of the photons energy goes.
I would guess that the diameter of the energy-wave sphere is the size of it’s wave length, or that the likelihood of being more than a wavelength away from its center is very low.
My questions are: How far apart can the slits be for the interference pattern to emerge? How close does the detector need to be to the slits to interrupt the wave pattern? That might help define the size of the “energy sphere”. Or it could blow this whole theory out of the water… it is late.
I may be way off on this, but it helps me imagine how it might work, based on my understanding.
Feel free to fight my ignorance, but be gentle…
Dag
I’ll try, but it’s going to be tough. I don’t wanna be a dick, but I’m pretty horrified.
Briefly, it looks to me like you just spent what is to me a baffling amount of time telling this board about a wide variety of wrong things you’ve made up about quantum mechanics.
Don’t get me wrong, I have no problem with guessing in some cases. If someone swooped down on you and forced you to take a test on this material, and this is what you came up with, I’d call it a good try.
But I admit I don’t understand why you felt the need to weigh in on a subject that you, by your own admission, don’t know much about, to give your best guess about what you imagine it is that might be going on. There are people on the board who actually can answer the question. I admit I’m not one of them, but they’re here. Why get in the way? I’m mystified.
There’s no rule that says you’ve got to give your opinion in every thread you read. Science isn’t a democracy of opinion; the views of those who know what they’re talking about actually are more important than the views of those who don’t-- especially in GQ. (I learned this early on, when I received a flame not unlike this one for doing something not unlike what you did. ;))
I’m sorry if that wasn’t too gentle. At least I skipped the Billy Madison quote.
Keep in mind were talking about the Copenhagen interpretation here. In this interpretation the wavefunction of the radioactive substance just forms a superposition with the wave function of the Geiger counter. This, of course, is based on presumption that the GC is ultimately composed of quanta. (How can it not be?)
So what collapses this combined superposed wavefunction?
Decoherence isn’t a part of the CI and is, by no means, a fully accepted formulation.
I was a dick. I had a rough week and took it out on another poster. Sorry. I normally try not to do that.
met⋅a⋅phor /ˈmɛtəˌfɔr, -fər/
–noun
2. something used, or regarded as being used, to represent something else; emblem; symbol.
I see that I did not qualify my post as I should have:
I am not saying this is the way the quantum world is, I am saying this is a metaphor for the way these things may happen.
I did freely use terms like “virtual particle” in a way that is not correct, as shorthand and as a metaphor, rather than using more words to explain what I really think, in unneeded detail.
It is difficult to be brief when I am talking about a way to visualize a concept in familiar ways to help understand one that acts in very unfamiliar ways. I also left out a bunch of detail to keep it from being way longer and totally unrelated to the OP.
As to the OP, the uncertainty exists only in the unstable particle. Schro was mistaken to try to entangle the Geiger counter with it (What would be the reason for the Geiger counter to entangle with that particular particle? How does its passive existence qualify as an “observation”?), and ridiculous to add the cat. He was trying to show QM’s bad logic, but instead illustrated that the quantum world resolves itself at a small scale. I mean, if you left the cat in there for a month, and the particle decayed on the first day, you would eventually be able to tell by the decay of the cat, there would be very little uncertainty about that smell!
The unstable particle could also be thought of as a wiggling ball at the edge of a group of balls representing the nucleus, and then at some point it wiggles free - decays. But that does not lend itself to a reason that there is a half life as well as comparing it to a chaotic wave or a highly variable number of units of energy. The “group of balls” metaphor is also only good for one kind of decay, and kinda dated. Besides, I did not want to be specific, this is more conceptual.
Another way to look at it might be that it is constantly shooting out “virtual” versions of the decay particle, and only 1 out of X of them turns into the “real” ejected particle. I can’t see much use for that metaphor, but there you go.
This helps me understand what entanglement is, if it does not help you, try to forget it. It is also interesting to see how far these metaphors can be stretched, and the reason that they can’t go beyond a certain point can also help to understand quantum stuff. For instance, thinking about why that last one is bad could be enlightening in itself.