Schrödinger's Cat

[Ginkgo]

Inquiring minds want to know what Schrödinger's cat is all about, how it relates to quantum mechanics, and superposition.

 

[Polaris]

Schrodinger's Cat is just a way of saying that you don't know which way something is until you settle the question by finding out. Finding out whether the cat is dead or alive is comparable to peaking out your window and finding out whether it's sunny or cloudy. Nothing mysterious is going on. Superposition is just a way of expressing the possible observations, along with their probabilities of occurring, as a single mathematical entity. It would be very fanciful to think that the cat is both alive and dead before you look at it, and that your looking at it causes it to die all the way or come entirely back to life.

It's worth mentioning that there are some observations, though, in which the means of making the observation does play a causal role on the thing being observed; e.g. your walking into a room full of people will allow you to see who is in the room, and your presence there as an observer will also effect what you see the people doing; some of them will likely glance in your direction, and more subtly, your vantage point itself will allow you to see some things while other things remain hidden from you. This kind of thing is a major point in physics, where the goal of an experiment is to get an observation of phenomena as they actually are, independent of any subjective influence. Scientists have found that this is impossible, because the tools that they use to make an observation will, like a person walking into a room and looking around him, always in some subtle way decide what they end up seeing. Schrodinger's Cat is not a very good way of illustrating this, though, because the cat is killed or given a reprieve by the box, not by the person who opens it. If the cat's life hinged (literally) on some mechanism in the hinges of the box, it would be a more apt illustration of how observing something determines, even if only in an extremely passive sense, what is observed.

 

[Octarine]

Inquiring minds want to know what Schrödinger's cat is all about, how it relates to quantum mechanics, and superposition.

How much understanding do you have of differential equations and basic statistics?

If not, do you have any stringed instruments?

Note about Polaris' post. It is not about human 'observation'. The superposition can decohere into a definite eigenstate due to quantum interactions, regardless of whether this interaction is formally observed or not. The interesting point is that we can only associate the system with a definite eigenstate at the moment of interaction. At other times, a superposition is a more natural assumption, at least if you discard classical notions of physics.

A statistical view is deemed acceptable in most sciences, so why not physics?

 

[SRT]

Schrodinger's Cat is just a way of saying that you don't know which way something is until you settle the question by finding out. Finding out whether the cat is dead or alive is comparable to peaking out your window and finding out whether it's sunny or cloudy. Nothing mysterious is going on. Superposition is just a way of expressing the possible observations, along with their probabilities of occurring, as a single mathematical entity. It would be very fanciful to think that the cat is both alive and dead before you look at it, and that your looking at it causes it to die all the way or come entirely back to life.

It's worth mentioning that there are some observations, though, in which the means of making the observation does play a causal role on the thing being observed; e.g. your walking into a room full of people will allow you to see who is in the room, and your presence there as an observer will also effect what you see the people doing; some of them will likely glance in your direction, and more subtly, your vantage point itself will allow you to see some things while other things remain hidden from you. This kind of thing is a major point in physics, where the goal of an experiment is to get an observation of phenomena as they actually are, independent of any subjective influence. Scientists have found that this is impossible, because the tools that they use to make an observation will, like a person walking into a room and looking around him, always in some subtle way decide what they end up seeing. Schrodinger's Cat is not a very good way of illustrating this, though, because the cat is killed or given a reprieve by the box, not by the person who opens it. If the cat's life hinged (literally) on some mechanism in the hinges of the box, it would be a more apt illustration of how observing something determines, even if only in an extremely passive sense, what is observed.

I thought that it had to do with quantum probability. I.e. that all things and events are possible but that by collecting more data we can conclude that certain things and events are more likely to be true than other things and events. That there are no definitive answers, only probabilities.

Wasn't Heisenberg the one who discovered that the act of observing particles in motion affect their trajectory? I don't think it has much to do with Schrodinger's cat. But then again my knowledge of physics is pretty poor.

*will wait for the smarties to come and clarify this concept

 

[Polaris]

Wasn't Heisenberg the one who discovered that the act of observing particles in motion affect their trajectory? I don't think it has much to do with Schrodinger's cat. But then again my knowledge of physics is pretty poor.

Heisenberg's discovery is related to Schrodinger's Cat in that they both illustrate the connection between observation and what is observed. The difference between them is that Heisenberg's discovery strictly concerns the role of observation, where Schrodinger's Cat is focused as much on that as it is on the state of uncertainty (called a superposition when mathematically formalized along with the probabilities of different resolutions for that state of uncertainty) that precedes an observation.

 

[Octarine]

Wasn't Heisenberg the one who discovered that the act of observing particles in motion affect their trajectory? I don't think it has much to do with Schrodinger's cat.

Not quite. Heisenburg's Uncertainty principle states that the precision of the position and momentum of the quantum particle in question is inherently limited. Increasing the precision of of the position decreases the precision of the momentum.

This was not a result of experiment, but Heisenberg's inequality (or non-commutativity as he originally derived it) along with related inequalities (based on other physical properties) drops straight out of the math.

The point is that the limits implied by the uncertainty principle are not 'experimental' limits, but physical limits.

So when electrons are visualised, according to QM we don't consider them to exist at a discrete point in space. There is however a probability density; areas where you are more likely to have an interaction with an electron. These interactions have limits with regards to the momentum and position as limited by the uncertainty principle.

Oh and the electron does not 'orbit' the nucleus either as popularised by the certain popular atomic icons. While the electron does have angular momentum analogous to that of an orbiting planet, as well as a spin analogous to a rotating planet, quantum mechanics cannot describe it as a point particle orbiting the nucleus.

None of the math in quantum mechanics was new. You will note how similar Heisenberg's inequality looks to this: http://en.wikipedia.org/wiki/Cauchy–Schwarz_inequality

Likewise, Max Born's "probability amplitude" interpretation of the wavefunction was natural as the math looks so similar to that of probability theory. (they called it probability density)

 

[Such Irony]

 

[Blank]

While this is some enlightening information, it may be best to drop some knowledge in Layman's terms.

 

[Ginkgo]

How much understanding do you have of differential equations and basic statistics?

If not, do you have any stringed instruments?

Note about Polaris' post. It is not about human 'observation'. The superposition can decohere into a definite eigenstate due to quantum interactions, regardless of whether this interaction is formally observed or not. The interesting point is that we can only associate the system with a definite eigenstate at the moment of interaction. At other times, a superposition is a more natural assumption, at least if you discard classical notions of physics.

A statistical view is deemed acceptable in most sciences, so why not physics?

I do have a 6 string guitar yes.

Ok, so I thought quantum objects were the only objects who's attributes change according to how they observed. I do have some basic statistics knowledge and yes I have experience with simple differential equations.

 

[Lateralus]

Inquiring minds want to know what Schrödinger's cat is all about, how it relates to quantum mechanics, and superposition.

It's a thought experiment Schrodinger came up with to try to disprove the Copenhagen interpretation.

 

[entropie]

Architectonic said it already, I will try to bring things into some context. I am no physicist so pardon incorrecntness.

Well first of all you have Heisenbergs uncertainity principle: you know that according to E = m * c² , every solid matter (m for mass, E for energy) is energy that got glued together. Then there is energy that hasnt become solid matter, like for example light. What light is made of, we dont know, but we describe its behaviour like that of a wave. If you use a sine wave-function you could describe the movement of light. So that means we have particles (matter) and waves.

The photon is a element of light. So what's a photon, a wave ? The thing is, depending on how you look at it, its either a wave or a particle. That's what Heisenberg was about. Heisenberg tried to capture a photon and when he did it was a particle. But when he didnt concentrate on a single photon but rather watched its movement, it behaved like a wave. That's called the Wave-particle-duality, which all particles inherit. For reference see Dr. Quantum ( Dr. Quantums Double Slit Experiment ).

Now three smart dicks, postulated the EPR-effect. That is the Einstein-Podolsky-Rosen effect. They said that they take a system with two particles which are one at the beginning. For example in an radioactive atom which is falling apart. Those two particles then leave the atom and travel in exactly opposite directions. They are quantenmechanically entagled. Now according to Heisenberg you can either only measure the place a particle is at or its impulse (movement). The impulse and the place can be shown as a vector. Like for example airplanes use it. A vectoir is a matrix of for example 4 numbers of which 3 are space coordinates and 1 is the impulse. Such a vector, applied to a quantum mechanical system is called the eigenstate. or eigenvector.

If we now dont measure neither the place nor the impulse of the particles, the result could be anything. Thats called the superposition of the eigenstate. In the moment of measurement, so when you take a picture, you'll only measure one eigenstate, namely the particle is next to Saturn or so.

So now back to the two particles, which are moving quantenmechanically entagled in the opposite direction. According to classical physic, I should be able to measure either place or impulse of both of the particles. But that is not the case. Fact is I can either measure the place of particle 1 and will get the place of particle 2 aswell or the impulse of both. So Heisenbergs theory now applies to two seemingly different particles. Instead of measuring place and impulse on could do the same with the particles spin but would get the same result.

This thought experiment was lately attested in reality by Niels Bohr I think to remember. It says that particles can be entangled in their quantum states and it says that something's very odd here and it's prolly our limited understanding so far why that is so.

Schrödinger back then now came and transfered this experiment into the macroscopic layer. He said if you put a cat into a box and put a radioactive nucleus into the box aswell, which will decompose but you do not know when. On decomposition it will trigger a geiger counter which then will smash a bottle with poison killing the cat. As long now as the box is closed, the cat is in superposition and can have the state of being dead or being alive. In the moment in which we oipen the box, the quantum mechanical system which the box resembles takes on one concrete eigenvector and therefore tells us where it is. That's the only way to find out if the cat is dead or alive.

Since thios is a game of probability you can say statistically that the cat is undead or dead-and-alive at the same time . Einstein said that this cant be all there is to it and commented it with the famous sentence "God doesnt play dice".

 

[Octarine]

I think the first thing to do when considering Quantum mechanics is to discard classical notions of particles and waves.

Even if all you can do is visualize the wavefunction similar to the set of harmonics of a vibrating string, this is better than those classical notions.
I might post in more detail now, but let us consider an idealized guitar string.

What happens when you pluck the string (provide the system with energy). You get standing wave harmonicsnot just at the fundamental, but in fact harmonics towards infinity (harmonics determined by the elastic potential and the boundary conditions). Note: A real guitar won't of course have harmonics up to infinity because of physical constraints. Anyway, if you were to touch the string at any point (except at the boundary points), the harmonic you detect could be any of the infinite range of harmonics. However, you are most likely to detect the fundamental harmonic. It clearly doesn't make much sense to say, hey, there must have been a particle that existed at that precise point. Nor is it a typical wave (since there are infinite harmonics and it isn't going anywhere). Hence classical notions of particles and waves don't really describe the system well.

Or course quantum mechanical systems have some bizarre aspects such as tunneling that are difficult to explain with the above analogy. Eg if you placed an infinitely deep node, and plucked only one side, you wouldn't see anything on the other side in the ideal guitar analogy (since the node must have a measurable width).

 

[tkae.]

The flaw with the experiment is the concept of the cat's fate causing no form of non-visual evidence.

If the cat dies, give it few hours and it's gonna start to smell.

If the cat lives, give it a few hours and it'll want water.

If you manage to find a way that the cat won't smell when it dies, then it will suffocate, and if it can somehow breathe, get water and air, and you still have nothing to go on, then that kind of scenario doesn't actually exist outside of a laboratory setting.

Soooo yeah

 

[Polaris]

Note about Polaris' post. It is not about human 'observation'. The superposition can decohere into a definite eigenstate due to quantum interactions, regardless of whether this interaction is formally observed or not. The interesting point is that we can only associate the system with a definite eigenstate at the moment of interaction. At other times, a superposition is a more natural assumption, at least if you discard classical notions of physics.

If you're required to interact with an object in order to determine which eigenstate it possesses, that illustrates the role of observation in exactly the way I described. Undoubtedly there are some cases where interacting with an object has negligible effects on it--this is a type of situation I outlined in my post--but there are also cases where the act of observation plays a tangible role on the object's state itself (by way of observation's means of observing). As far as I can tell, Copenhagen's ideas are a scientific elaboration on this latter kind of case, whereas Schrodinger's Cat illustrates a case in which there is no decisive role being played either by observation's means of observation or by any other physical entities; the object's state at such a moment can only be determined as a range of mutually exclusive possibilities, called a superposition.

 

[Octarine]

My point was to shift away from unnecessary notions of human influence and towards considering the underlying interactions involved. It is true that such interactions must have occurred for a human to make an observation. But my point was that such equations describe the limitations of physical interactions independent of human action.