What makes schrodinger cat quantum?

[ArielGenesis]

Hi I am learning quantum physics in 2nd year
i want to know what makes Schrodinger cat quantum?
how do we ended up in the Copenhagen interpretation?

i.e.
probability density function = 0.1; 0<x<10; =0 everywhere else
we could say that the particle is simply moving very fast (ignoring relativity)
and so its purely classical
I do understand that the way we interpreted it is that the particle is everywhere between 0 to ten and the fact that we measure it cause it to collapse. but what i don't see is how we come to that conclusion.

why do we conclude that Schrodinger cat is both alive and death?

thx in advance.

 

[Count Iblis]

Just like special relativity replaced classical mechanics, so did quantum physics replace classical mecanics. So, it should be the case that in the "classical limit" quantum mechancs effectively becomes classical mechanics analogous to how special relativity becomes the same as classical mechanics at low velocities.

However, this is not as straightforward, because one can think of scenarios like Schrödingers cat-like superpositions which are clearly non-classical but still exist in the macroscopic domain.

One then has to show that in practice such superpositions don't occur. The Copenhagen interpretaion is nothing more than an ad hoc declaration that the wavefunction will collapse. It is not a detailed theory explaining why and how, giving the microscopic laws of physics, this (effectively) will happen.

The effective wavefunction collapse can be explained by so-called "decoherence", see these articles:

http://arxiv.org/abs/quant-ph/0006117

http://arxiv.org/abs/quant-ph/0204129

http://arxiv.org/abs/quant-ph/0205108

 

[Irrational]

the cat isn't 'quantum'. it's the radioactive decay that is governed by quantum mechanics. if the geiger-counter detects radiation, then the vial is broken, killing the cat. since the radioactive decay is probabilistic, we cannot say whether the geiger-counter detects it until we open the box and observe what has happened.

this is one of the problems i have with this experiment. the cat is not physically, both alive and dead. however, we cannot deduce whether it is dead or alive until we look in the box. it's a silly thought experiment to be honest.

 

[Count Iblis]

As far as we know, the whole universe is governed by quantum mechanics. The thought experiment exposes a potential problem with how the classical world is supposed to effectively arise, as the macroscopic superpositions are never observed, yet they can, in theory, exist.

It is not that the cat is both dead and alive, just like an electron being in a superposition is not at two places at once. It is a superposition between two states which is a new single particle state that has no classical analogue (which explaines interference phenomena).

So, as long as the box is perfectly isolated, you could, in principle, verify that the cat is in a superposition of "dead" and "alive" by doing a very very complicated interference experiment. In practice this is nearly impossible.

 

[ArielGenesis]

@irrational: yes i know that the cat is not 'quantum' per se.

so the copenhagen interpretation is merely and interpretation? its not proven yet? I am currently too busy to open the links but thx.

and thus, the exact process of collapsing is simply currently unexplainable?

 

[meopemuk]

Yes, the cat is in superposition of "dead" and "alive" states inside the box. What's wrong with that? You may say "I've never seen a half-dead half-alive cat in my life". But you have never looked inside a closed box too. If you had such a chance, then the box was not properly closed.

 

[ArielGenesis]

I am at the point where quantum mechanic make sense, yes i can understand the cat being in the super position of life and death. what I don't understand is why we ended up at this conclusion instead of just assuming for hidden variable?

 

[diazona]

It's been proven that hidden-variable theories can't properly describe reality - Bell's theorem, I think, and associated experiments. I don't remember the details right now...

 

[meopemuk]

I am at the point where quantum mechanic make sense, yes i can understand the cat being in the super position of life and death. what I don't understand is why we ended up at this conclusion instead of just assuming for hidden variable?

You are welcome to assume that "hidden variables" exist. In this case, decays of radioactive atoms would be proven to be not random, but controlled by some kind of hidden atomic "alarm clock". Then one would be able to predict exact timing of such decays, and one would be able to say exactly (without looking inside the box) whether the cat is alive or dead.

The only problem is that so far nobody was able to design a "hidden variable" theory that can predict the timing of decays. Not even at very poor level of accuracy. In 80+ years this idea hasn't moved even 1 inch closer to experimental verification. This is a nice dream, but it hasn't been supported by any real data yet.

 

[meopemuk]

In order to understand quantum mechanics and avoid paradoxes one needs to note clear distinction between a "physical mechanism" and a "mathematical recipe". Quantum mechanics does not talk about "physical mechanisms". It only provides "mathematical recipes".

In the Schroedinger's cat case QM does not say that the cat is in a superposition of two states. It does say that we don't know in which state the cat will be found once the box is opened. It says that there is a certain probability of finding the cat alive and another probability of finding a dead cat. If you ask "what are these probabilities?" quantum mechanics gives you a "mathematical recipe" for calculating them. This recipe involves certain ingredients, which have no relationship to the observed reality: Hilbert space, state vectors, Hermitian operators of observables, projections, superpositions, etc. If you follow this recipe, you finally find the values of probabilities, which agree well with experimental results (if you repeat the experiment sufficiently many times). That's all quantum mechanics can do. Don't accept QM as a "model of reality". Think of it as no more (and no less) than a "mathematical recipe" for calculating probabilities of observations.

If you ask "what actually happens to the cat while it's inside the closed box?", quantum mechanics has no answer. Currently there is no reasonable theory that can answer that question. There are various speculations, but they are not credible, because they cannot be verified by experiment, simply because the question is formulated that way (the box is supposed to be closed, and we are not allowed to look inside it).

 

[Bob_for_short]

What makes Schrodinger cat quantum?

Cats are quantum by definition. Any cat is represented by a linear superposition of kets |k>, where k is a cat momentum vector. Any cat is always in a superposition state: you never know where it will go next. That makes them funny. Being funny is not classical feature but quantum. Passive observation does not destroy the superposition state. Active interaction changes the coefficients of the linear superposition: it's a typical quantum dynamics. They perfectly fit a double slit experiment.

Cats are always alive. There are no dead cats as there are no decayed µ-mesons. According to some, cats have up to 9 lives.
Cats love to hide in boxes. Cats are pets and kets.

Bob.

 

[Count Iblis]

In order to understand quantum mechanics and avoid paradoxes one needs to note clear distinction between a "physical mechanism" and a "mathematical recipe". Quantum mechanics does not talk about "physical mechanisms". It only provides "mathematical recipes".

In the Schroedinger's cat case QM does not say that the cat is in a superposition of two states. It does say that we don't know in which state the cat will be found once the box is opened. It says that there is a certain probability of finding the cat alive and another probability of finding a dead cat. If you ask "what are these probabilities?" quantum mechanics gives you a "mathematical recipe" for calculating them. This recipe involves certain ingredients, which have no relationship to the observed reality: Hilbert space, state vectors, Hermitian operators of observables, projections, superpositions, etc. If you follow this recipe, you finally find the values of probabilities, which agree well with experimental results (if you repeat the experiment sufficiently many times). That's all quantum mechanics can do. Don't accept QM as a "model of reality". Think of it as no more (and no less) than a "mathematical recipe" for calculating probabilities of observations.

If you ask "what actually happens to the cat while it's inside the closed box?", quantum mechanics has no answer. Currently there is no reasonable theory that can answer that question. There are various speculations, but they are not credible, because they cannot be verified by experiment, simply because the question is formulated that way (the box is supposed to be closed, and we are not allowed to look inside it).

I don't agree, the problem is not that the box is closed, but rather that the system decoheres very fast. So, you can't keep it isolated for long enough to veryfy that the system is in a non-classical state. For smaller system we can verify that non classical superpositions exist.

One has to invoke new physics to explain why the formalism of quantum mechanics that can be applied to the micro world would not apply in principle to the macro world. The fact that one cannot explicitely measure any deviation of classical physics in the macroworld is not a good argument. You could just as well postulate, without any basis in physics, that above 100,000 K thermodynamics is invalid and then defend yourself by arguing that no one has ever been able to measure the temperature of the Sun's interior directly using an ordinary thermometer.

 

[Count Iblis]

If your cat is dead, try measuring the observable:

[|dead> + |alive>][<dead| + <alive|]

 

[meopemuk]

For smaller system we can verify that non classical superpositions exist.

Could you give an example when a microscopic system was found experimentally in a superposition state?

Each time we measure position of an electron, we obtain a single value, i.e., one well-defined dot on the photographic plate. We never see a "superposition of dots" or something like that. The need for superposition arises from the fact that if we repeat position measurements many times in identical conditions, then each time we'll find different results. So, we introduce an abstract mathematical idea of the superposition of electron states. Such superpositions can not be seen directly in experiments.

 

[Count Iblis]

http://arxiv.org/abs/cond-mat/9908283

http://arxiv.org/abs/cond-mat/0305461

 

[meopemuk]

http://arxiv.org/abs/cond-mat/9908283

http://arxiv.org/abs/cond-mat/0305461

This looks like a typical two-level quantum system, which shows time-dependent oscillations between the two states $|0 \rangle$ and $|1 \rangle$. Note that each individual measurement can find the system either in the state
$|0 \rangle$ or in the state $|1 \rangle$. A single measurement can never find the system in the "superposition" of the two states. The idea of "superposition" is prompted by the fact that if we repeat the experiment many times in identical conditions, we sometimes find the system in the state $|0 \rangle$ and sometimes in the state $|1 \rangle$. Perhaps this is what the authors meant by writing "The switching probability is obtained by repeating the whole sequence of reequilibration, microwave control pulses and readout typically 5000 times."

So, the experimental fact is that measurement results jump unpredictably between $|0 \rangle$ to $|1 \rangle$. In order to describe this fact, quantum mechanics introduces the idea of "state superposition". This idea is a part of the "mathematical recipe" for calculating (switching) probabilities. However, experimentally, such "superposed" states are never observed. The coefficients of this superposition vary continuously with time, as can be seen in the experiment. And this variation can be computed with the help of the Schroedinger equation. Nevertheless, results of individual measurements remain (a) classical (no superposition) and (b) unpredictable.

 

[Bob_for_short]

...superpositions can not be seen directly in experiments.

If a single measurement finds the system in one state proper to some Hamiltonian, this same state may be considered as a superposition of states of another Hamiltonian. In this sense a superposition is as observable as a pure state.

Bob.

 

[meopemuk]

Hi Bob,

with my statement I meant the following: In experiments one measures values of certain observables (position, spin, energy, etc. depending on the setup). Each time a measurement is made, the experimentalist finds a single unique value of the observable. He never finds a "superposition" of two or more values. The electron cannot be observed in two places at once.

All statements about eigenstates, basis sets, superpositions, colapse, etc. should belong to the "mathematical recipe" of quantum mechanics. They should not be confused with "physical mechanism".

 

[Bob_for_short]

I am afraid that one single observation is quite meaningless in the quantum world: it says nothing about probabilities. Only a huge set of results reveals the real probability distribution. Theoretically it is most essential to predict this distribution than a single event if the latter is no way reproducible by its nature.

Bob.

 

[meopemuk]

I am afraid that one single observation is quite meaningless in the quantum world: it says nothing about probabilities. Only a huge set of results reveals the real probability distribution. Theoretically it is most essential to predict this distribution than a single event if the latter is no way reproducible by its nature.

I agree.

My point is this: if one observation has found the electron at point x and the next observation (in identical circumstances) has found the electron at point y, does this mean that we have observed the electron in the "superposition state"? My answer is "no". The "superpositon state" is a mathematical abstraction, but not physically observed reality.

 

[Bob_for_short]

My point is this: if one observation has found the electron at point x and the next observation (in identical circumstances) has found the electron at point y, does this mean that we have observed the electron in the "superposition state"? My answer is "no". The "superposition state" is a mathematical abstraction, but not physically observed reality.

We can always say that we observe such an non-reproducible events just because the electron (photon, whatever) is in the superposition state. It makes sense and does not contradict to a single observation.

Vladimir.

 

[meopemuk]

We can always say that we observe such an non-reproducible events just because the electron (photon, whatever) is in the superposition state. It makes sense and does not contradict to a single observation.

Yes, we certainly can do that. This is a respectable point of view. However, then we shouldn't complain about the "incomprehensible" wave function collapse, and we shouldn't be surprised by the statements about half-alive half-dead cats. They are just direct consequences of our assumption about the physical existence of superposition states.

Another respectable point of view is that we shouldn't even concern ourselves with questions like "what is the physical state of the electron/photon/cat... before the measurement?" We may remain agnostic about the exact physical nature of such states. We may simply say that results of measurements in such states are unpredicatable/probabilistic. If numerical values of these probabilities are needed, we can use the mathematical machinery of quantum mechanics to get them.

 

[Count Iblis]

This looks like a typical two-level quantum system, which shows time-dependent oscillations between the two states $|0 \rangle$ and $|1 \rangle$. Note that each individual measurement can find the system either in the state
$|0 \rangle$ or in the state $|1 \rangle$. A single measurement can never find the system in the "superposition" of the two states. The idea of "superposition" is prompted by the fact that if we repeat the experiment many times in identical conditions, we sometimes find the system in the state $|0 \rangle$ and sometimes in the state $|1 \rangle$. Perhaps this is what the authors meant by writing "The switching probability is obtained by repeating the whole sequence of reequilibration, microwave control pulses and readout typically 5000 times."

So, the experimental fact is that measurement results jump unpredictably between $|0 \rangle$ to $|1 \rangle$. In order to describe this fact, quantum mechanics introduces the idea of "state superposition". This idea is a part of the "mathematical recipe" for calculating (switching) probabilities. However, experimentally, such "superposed" states are never observed. The coefficients of this superposition vary continuously with time, as can be seen in the experiment. And this variation can be computed with the help of the Schroedinger equation. Nevertheless, results of individual measurements remain (a) classical (no superposition) and (b) unpredictable.

The system can be measured to be in the state

1/sqrt(2)[ |0> + |1>]


meaning that it is verifiable not in either |0> or |1>. Of course the particular measurement you need to indicate that will itself involve some other macroscopic object to be ina well defined classical state. However, that then rules out that the current in the ring is flowing in either the clockwise or anticlockwise way, it is really in the superposition of these two classical states.

Such superpostions are completely different from an unknown classical state that can either be in one of the two states. Such a state can be described by a density matrix and it is possible to tell the diferece between a mixed state and a pure state.

 

[ArielGenesis]

so a half alive half dead cat only exist in the qunatum mecahanist's mind

mathematically, there is nothing wrong with it, physically, it predicts the trends properly and that's just it?

 

[meopemuk]

so a half alive half dead cat only exist in the qunatum mecahanist's mind

mathematically, there is nothing wrong with it, physically, it predicts the trends properly and that's just it?

Yes, I think this is a reasonable summary.

 

[Bob_for_short]

What makes Schrödinger cat quantum?

Box! In a box even classical waves get quantized!

 

[Asok_Green]

Could there be a little more discussion about whether QM says the cat really is in superposition of both states? I was under the impression that the whole point of the thought experiment was to illustrate that if we could shield a system from quantum decoherence, superposition could extend to the macroscopic. If that's not the case, I am ignorant of the purpose of the thought experiment.

 

[meopemuk]

superposition could extend to the macroscopic.

Superposition cannot "extend to the macroscopic", because it does not exist even for smallest microscopic particles. Each time we measure an observable (position, momentum, spin, etc.) of the electron we obtain a definite number. We never see the electron "half here and half there". So, we never see superpositions directly.

The problem is that if we repeat measurements of the observable many times on identically prepared electrons, we may measure different values of the observable each time. The idea of "superposition" was invented to explain/describe this (apparently random) effect. This invention exists only in minds of quantum physicists.

 

[Count Iblis]

Each time we measure an observable (position, momentum, spin, etc.) of the electron we obtain a definite number.

Yes, but momentum and position do not commute. An electron in a definite momentum state is in a superposition of many different position states. It is noit the case that the electron has some definite position and we don't know what that position is. Such a so-called "mixed state" can be distuinguished from a genuine superpostion, e.g. via interference experiments.

 

[meopemuk]

Yes, but momentum and position do not commute.

This is true.

An electron in a definite momentum state is in a superposition of many different position states.

We can say for sure only the following: "If we prepare an ensemble of electrons such that momentum measurements yield the same value for each member of the ensemble, then position measurements for each member will be scattered all over the place". This is what we see directly in experiments, so we can be 100% sure that this statement is correct.

However, from the point of view of theoreticians this statement is not useful for developing a predictive theory. So, they replace it with another statement "before the measurement the electron is in a definite momentum state, which is a superposition of different position states". This theoretical statement is good for formulating the mathematical recipe of quantum mechanics, but it is important to understand that superpositions are mathematical abstractions, and they have been never seen in real life.

If we always make a clear separation between what is actually observed in experiments (definite values of observables measured in ensembles of identically prepared systems) and what is part of a mathematical model (e.g., superpositions, Hilbert spaces, Hermitian operators, etc.), then all inconsistencies and paradoxes of quantum mechanics can be easily resolved.

 

[diazona]

Well, if you prepare an ensemble of Schrödinger's cats in boxes, then measurements of the survival of each cat after a predetermined amount of time will be all over the place. (Some alive, some dead) So by that argument, it's just as valid to say that the cat is in a superposition of $\vert\text{alive}\rangle$ and $\vert\text{dead}\rangle$ as it is to say an electron is in a superposition of two states. (Of course, $\vert\text{alive}\rangle$ and $\vert\text{dead}\rangle$ are not single quantum states, which complicates the picture...)

 

[Bob_for_short]

What makes Schrödinger cat quantum?

Maybe Schrödinger himself? He was quite a quantum geek.

 

[Count Iblis]

The density matrix |p> <p| describes the ensemble of the set of identically prepared electron states in momentum |p>. In the position representation this density matrix is:

rho = Integral d^3x d^3y |x><x|p><p|y><y| =

1/V Integral d^3 d^3y exp[i p(x-y)] |x><y|

where V is the volume of the box each electron is in.

rho has off diagonal components, which means that one can observe coherence effects in the statistics of measurements. In contrast, the density matrix of a ensemble of electrons that all have some definite but random position in the box is:

rho = 1/V Integral d^3 x |x><x|

 

[meopemuk]

Well, if you prepare an ensemble of Schrödinger's cats in boxes, then measurements of the survival of each cat after a predetermined amount of time will be all over the place. (Some alive, some dead) So by that argument, it's just as valid to say that the cat is in a superposition of $\vert\text{alive}\rangle$ and $\vert\text{dead}\rangle$ as it is to say an electron is in a superposition of two states. (Of course, $\vert\text{alive}\rangle$ and $\vert\text{dead}\rangle$ are not single quantum states, which complicates the picture...)

Yes, I don't see any significant difference between superposition of cat states and superposition of electron states. Both of them are imaginary superpositions that exist only in minds of theoreticians. Each time we measure electron's position we get a definite value. Each time we look at a cat we see it either dead or alive.

 

[meopemuk]

The density matrix |p> <p| describes the ensemble of the set of identically prepared electron states in momentum |p>. In the position representation this density matrix is:

rho = Integral d^3x d^3y |x><x|p><p|y><y| =

1/V Integral d^3 d^3y exp[i p(x-y)] |x><y|

where V is the volume of the box each electron is in.

rho has off diagonal components, which means that one can observe coherence effects in the statistics of measurements. In contrast, the density matrix of a ensemble of electrons that all have some definite but random position in the box is:

rho = 1/V Integral d^3 x |x><x|

Yes, there are two sources of probabilities in the formalism of quantum mechanics (and in nature). One is the regular classical probability, which simply results from our incomplete specification of the preparation process (like when we throw a die on the table). This probability is described by "mixed states" in QM.

The other (intrinsically quantum) probability remains even when the preparation of the system's state is fully controlled. Quantum mechanics does not explain the origin of this randomness. It simply provides a mathematical tool for its description and analysis. The states in which the "classical" randomness is completely eliminated are called "pure states". I was talking only about such "pure states" in my posts.