I’m sure many of you are familiar with the Schrödinger’s Cat thought experiment. (Note: thought experiment . . . no cats were harmed, yada yada.) First, you put a cat in a box. Then you take a single atom of some radioactive isotope, and set up a mechanism so that if the atom decays while the mechanism is turned on, it will trigger and kill the cat. You set the mechanism to run for one half-life of the isotope before turning off (so there will be a 50% chance of a decay and a dead cat), and you then leave the room. You wait for the mechanism to do its thing. Here’s the weird part: according to quantum mechanics, until you observe the atom, it is in a superposition of decayed and undecayed states. This means that until you observe the cat, he’s in a superposition of alive and dead states. This is often used as an example of the bizarre consequences of quantum mechanics.
Of course, the moment you look into the box you see either a living or a dead cat. And the process of making this observation collapses the wave function of the cat to either the “living” or “dead” state, and likewise collapses the wave function of the atom to either the “decayed” or “undecayed” state.
At least, this is how the thought experiment has usually been presented to me.
My question is, why doesn’t the cat’s observation count? I mean, either the cat observes himself to be still alive, or he doesn’t, right? Isn’t this just as much a measurement as me looking in the box? I mean, surely quantum mechanics doesn’t distinguish between human observations and cat observations, does it? In fact, it seems to me that even the mechanism that has to either kill or spare the cat is making a measurement, and that this is just as much an observation as anything a person could do. So is the whole Schrödinger’s Cat thought experiment a bunch of nonsense, and really you never get a superposition of living and dead cats? Or am I misunderstanding what the thought experiment is supposed to convey?
I think Schrödinger intended the Cat example to demonstrate that the whole concept of superposition was absurd. No-one thinks that any macroscopic object (let alone a cat) can exist in a state of superposition, but quantum entities can.
The collapse-of-the-waveform problem (what exactly causes the cat death or not) continues to be a. . . problem.
You want real quantum weirdness? Look for texts on the ‘EPR paradox’ and ‘Bells inequality’.
Once more: S.C. steps back and waits for the physicists turn up and make things all complicated
[QUOTE=Small Clanger]
I think Schrödinger intended the Cat example to demonstrate that the whole concept of superposition was absurd. No-one thinks that any macroscopic object (let alone a cat) can exist in a state of superposition, but quantum entities can.
The collapse-of-the-waveform problem (what exactly causes the cat death or not) continues to be a. . . problem.
You want real quantum weirdness? Look for texts on the ‘EPR paradox’ and ‘Bells inequality’.
This is where It gets wonky for me, exactly how or why can quantum entities exist in a state of superposition? What is the mechanism that allows for this to occur?
There was a description in (Nature? ??) magazine some time ago that seemed to be clearly stating that, as long as there is no way of observing the cat or the particle, and no way, direct or indirect, of finding out the state of affairs, the cat is definitely not alive and definitely not dead. That we know for a fact the cat has entered a third state, the indeterminate. And the atom has definitely not decayed and also is definitely not non-decayed, it is indeterminate instead.
And indeterminate, of course, has never been observed by anyone except maybe an all-knowing entity such as God.
I have problems with this. I could understand the wording of this if they changed it to: the particle is in an unknown state (call it indeterminate if you want, but the definition would have changed), it’s in a don’t-know state, a can’t-know state, a don’t-care-because-it-makes-no-difference state, until some observation finds what it is. But it’s in one of two real states, not a mysterious third one.
See, I understand what you are saying. I don’t understand the “how” of it. What proofs are the Ubiquitous “THEY” using to explain this phenomenon? How do they know this? It makes me nuts. It’s like asking ‘if a tree falls in a forest…etc.’ ::::::::::::::banging head against wall:::::::::::::::::
You don’t need a decaying atom to create an “unknown” state. Flip a coin and catch it in your hand. Before you open your hand up and observe whether it is heads or tails, it’s in an unknown state. It is both heads and tails. It is also Not heads OR tails. It’s not until you observe it and collapse one of the wave forms that it is truly one or the other…
As I’ve always understood it, the cat is in neither state. That doesn’t mean a third state has been created - it just means that without an outside observer (hence the cat’s POV being irrelevant), there is no conclusion to the experiment. The how of it is that at the quantum level there are no results until it is measured (aka observed.)
As for using a cat, Schrödinger was merely using an object with which people could identify. He could have easily substituted a goat, a flaming pig, or William Shatner.
Look, the particle isn’t in one state or the other prior to observation. It’s in a superposition of two states. The act of making a measurement actually changes the state of the particle, so that rather than being a superposition of eigenstates it’s in a particular eigenstate of whatever measurement you’re making.
In layman’s terms, an eigenstate means “a state that the measurement doesn’t change.” So, say I want to measure whether a particle is spinning clockwise or counterclockwise around a certain axis. In reality, when we talk about the “spin” of a particle, we don’t mean that it’s spinning in the classical sense – it’s not – but I’m trying to give a simple example that is comprehensible to those who haven’t studied much physics. The true state of the particle might be 70% clockwise / 30% counterclockwise. That means that if you put a particle in that state and measured which way it’s spinning, you’d measure clockwise 70% of the time, and counterclockwise 30% of the time. However, let’s say you make the measurement, and find out it’s spinning clockwise. The act of making this measurement changes the state of the particle so that it is now in an eigenstate of our “which way is it spinning” measurement. So, each subsequent time that we make the measurement, the particle will still be spinning in the clockwise direction, and the state won’t change (since it’s an eigenstate). So it’s not that we didn’t know which way the particle was spinning – it wasn’t in a state of definite spin before we made the measurement! In other words we aren’t just measuring something, we’re changing something!
To those who are having trouble wrapping their heads around this, my suggestion would be to stop thinking of particles as actual particles in the classical sense. In quantum mechanics, a particle can be represented by a wave packet – basically, think of a wave that has its amplitude maximized at a certain point, with the amplitude falling off to zero on all sides of that. So the envelope of the wave is like a three dimensional gaussian distribution (a “bell curve”). Now, suppose I asked you “Where is this wave?” Your answer would have to be “Well, it doesn’t have a single defined position – it just has different amplitudes at different points in space.” So, there is some uncertainty in it’s position – nothing so strange about that. Now, suppose you tried to measure the exact position of the wave (even though it doesn’t really have one). You’d be most likely to measure it right at the peak of the distribution – but there’s a chance you’d measure it a little to one side or another from the peak. We can only talk about the probability of you measuring a certain position.
The weird thing in quantum mechanics is that your measurement changes the wave. After you measure it to be at a certain point, the wave function collapses to an infinitesimally narrow spike at that point (called a Dirac delta function.) So, at that moment of your measurement, the wave function really does represent a particle located at a single point in space. After the measurement, the delta function gradually expands back out into a wave packet.
My point is, there’s nothing weird about talking about something in a superposition of states and whose properties don’t have definite values. I can construct an ordinary macroscopic wave packet (out of say, sound waves) that has neither definite position nor definite momentum. The weird thing in quantum mechanics is that if we measure its position or momentum (or anything else) the function changes so that that particular measured quantity does have a definite value – namely whatever one we measured.
Getting back to my original post, I don’t buy the excuse that the Schrodinger’s Cat thought experiment is just an analogy to what happens on the quantum level. I have always had this presented to me as an actual hypothetical example of how one can create a superposition of states on a macroscopic level. If it were just an analogy, you could just say “Particles in quantum mechanics are like cats that are both alive and dead.” But this isn’t what is said. Instead, a specific way of producing a cat that is “both alive and dead” is described. I’m saying, this seems like bull****, that wouldn’t give you a cat that’s both alive and dead, because an observation has been made by both the cat and the apparatus itself in the process. I’m still waiting for someone with a physics degree to come in here and tell me definitively whether I’m right or I’m wrong.
I’m not trying to denigrate the people who have already replied – I appreciate your responses – but I still feel like my original question hasn’t been answered in any sort of definitive way. I’m hoping for something like “Yep, that’s an observation” or “No, that doesn’t count as an observation, because an observation must satisfy this specific criteria that that fails to meet.”
Actually, erislover gave me a pretty good definition of an observation.
This is basically what I thought as well. But if so, the oft repeated claim that the thought experiment describes a “cat which is both alive and dead” is total BS, isn’t it? It just describes a means of killing a cat that will have a 50% success rate, and this is not profound. If that’s all we’re doing, I might as well let kitty play Russian roulette with a half-emptied revolver, and leave quantum mechanics out of it.
It is in fact either heads or tails. And just one of those. There is no wave form to collapse. As Small Clange put it so accurately to begin with…Shrodinger’s actual point to this thought experiment was to convey the absurdity of relating quantum particle level paradoxes to macro level reality.
Sure it is. Because if you don’t leave quantum mechanics out of it, it forces you to think about the quantum level of reality where things work in ways that make no sense one our macro level. But apparently that’s how they do work. Shrodinger is just providing a metaphor for people to understand just how alien the micro level really is.
I’m not so sure of this. If (as I suspect) an observation truly means any interaction whose result is dependent on the state of an object, then the light bouncing off the coin as it flips is observing it’s state, the air being displaced by the coin is observing its state, etc.
The difference between a coin (made up, obviously, of very many particles) and a single subatomic particle is that a single particle can fly through space for a while and not interact with anything. In other words, they can truly go unobserved. Heck, there are millions (thousands? billions? I don’t know the order of magnitude) of neutrinos flying through you right now, and not interacting with anything.
It seems absurd to me to claim that the state of a coin (or anything else) is changed not by the light bouncing off of it, but by the fact that at some later time that light happens to strike the eye of a sentient being.
In fact, even if I think observation means “observation by a sentient being” (say, myself), the state of the coin is changed (to whatever the observed state is) at the time the light I’m seeing struck the coin (since I only have knowledge of its state at that time), not at the current time. But if this claim is true, my seeing the coin caused the state to change at some earlier time. This isn’t just absurd, it’s causality violating.
I assume you mean “sure it is profound” not “sure it is B.S.” (a little ambiguous given the post you were replying to.) But I don’t see how. Either you have a living cat or a dead cat, never a superposition of cats, right? (Or are you saying we do have a superposition of cats, in which case my question “why doesn’t the cat’s own observation collapse it into a state of definite deadness” still needs an answer.) But if we don’t have a superposition of living and dead cats, then how is the macroscopic cat state at all analogous to anything happening on the microscopic level? It’s just an ordinary cat that might or might not be dead, with nothing quantum mechanical about it.
Let’s try, how this indeterminate state is used by physical scientists.
We can see that a lot of very smart people who have dedicated their lives to this field will tell us that a particle can be decayed and un-decayed at the same time, or spin can be 70% clockwise and 30% counter- at the same time, until it’s observed or interacted with.
Why don’t they just use statistics? Ie, the spin has a 70% likelihood of being clockwise when it’s measured, or of these thousand particles, approx. 700 spin clockwise? Or, this particle has a curve of probability of location, and the curve is shaped like XXX until we measure it? (sorta like playing Battleship).
What makes the indeterminacy approach be more desirable than the statistical approach?
The statistical approach fails to capture all of the information about the quantum system. This is kind of hard to describe, but it relies on the fact that there are several different measurements you could make on a system, each of which will disturb the system so as to preclude making any of the other measurements. In particular, we can sometimes choose a measurement of a quantum system that will always give the same answer, even if other measurements only give statistical information. This means that a quantum superposition is distinguishable from a statistical mixture.
A more detailed answer: For a particle with “spin,” think of the “spin” as counterclockwise rotation around some axis. (The particle isn’t really spinning, of course, but for the purposes of this post you can think of it that way.) The “counterclockwise” rotation is then spin about an axis pointing vertically upward; the “clockwise” rotation is spin about an axis pointing down. But the particle could also be spinning about an axis pointing to the left, or up and to the right, or in any other direction.
It turns out that if you take a particle that’s really spinning along one axis “u”, and measure its spin along a different axis “v”, you will always find that the particle is spinning either “up” along v or down along v (that is, spinning about v or spinning about -v); you will measure each of these with a probability dependent on the angle between u and v. If u and v are perpendicular, then the probability is 50%-50%; but if u and v are the same, then you’ll always measure spin along v, and if u and v are oppositely directed, you’ll always measure spin along -v.
So if you measure the spin along the z axis for a particle whose spin is “really” along the x axis, you’ll get a 50/50 mix of “up” and “down.” But you can’t think of this particle as a statistical mix of 50% z-up and 50% z-down, because if you measure the same particle along the x axis, you’ll always measure “up”.
