Schrodinger's Cat radioactive source

[TheScienceOrca]

http://en.wikipedia.org/wiki/Schrödinger's_cat


I don't understand, if the radioactive source is put in there then of course the Geiger counter will detect radioactivity so we know the cat must be dead?

 

[phinds]

http://en.wikipedia.org/wiki/Schrödinger's_cat


I don't understand, if the radioactive source is put in there then of course the Geiger counter will detect radioactivity so we know the cat must be dead?

What did you not understand about the article's statement:

there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none;

 

[TheScienceOrca]

What did you not understand about the article's statement:

Thanks now I understand, I thought it would always be radioactive.



Doesn't this simply mean that we just don't know whether it's dead or alive?

Not that it's both dead and alive?


Thanks for the help

 

[phinds]

Thanks now I understand, I thought it would always be radioactive.

It IS always radioactive, just at a low level.

Doesn't this simply mean that we just don't know whether it's dead or alive?

Not that it's both dead and alive?Thanks for the help

Schrodinger came up with the cat thing to show how absurd the Copenhagen interpretation of QM can be sometimes. Yes, the cat is always either alive or dead, we just don't know which until we open the box and if it's dead, we don't know when it died (unless we put a timer on the counter).

Also, the moon really IS there whether it's being observed or not.

 

[TheScienceOrca]

It IS always radioactive, just at a low level.




Schrodinger came up with the cat thing to show how absurd the Copenhagen interpretation of QM can be sometimes. Yes, the cat is always either alive or dead, we just don't know which until we open the box and if it's dead, we don't know when it died (unless we put a timer on the counter).

Also, the moon really IS there whether it's being observed or not.

I see, so it could be alive or it could be dead.


When they said the statement it could be dead or alive at the same time I thought they meant both states at the same time. The cat can only be in one state at a time, but since we don't know it's state; it COULD be alive or it COULD be dead.

That is how they should state it so there is no confusion.

Correct me if I made any mistakes in my understanding.

 

[StevieTNZ]

Also, the moon really IS there whether it's being observed or not.

How do you come to that conclusion?

 

[PeterDonis]

The cat can only be in one state at a time, but since we don't know it's state; it COULD be alive or it COULD be dead.

No, it's more counterintuitive than that. The cat can only be in one state at a time, yes. But the states |ALIVE> and |DEAD> are *not* the only possible states the cat can be in, according to quantum theory. It can also be in a more general state that, mathematically, we would write as

|C> = a|ALIVE> + b|DEAD>

where a and b are complex numbers whose squared moduli add up to 1. (In general, a and b are time dependent; in the setup as Schrodinger originally gave it, a^2 decreases as time goes on, while b^2 increases). The point is that this general state |C> is a state which is a perfectly valid quantum state, according to the theory, but in which the cat is neither alive nor dead, nor is it correct to say that the cat "could" be alive or "could" be dead in this state. This state |C> that the cat is in during the experiment is simply a state that has no classical analogue, and no classical description like "cat alive" or "cat dead" or even "cat could be alive or could be dead".

We observe small objects like electrons in states like this all the time; but Schrodinger's point with the cat thought experiment was to raise the question of whether things like cats can really be in such states. (IIRC he thought they couldn't, and intended his thought experiment as a reductio ad absurdum of the claim that quantum mechanics was a complete theory.)

 

[bhobba]

How do you come to that conclusion?

I think he is referring to the many threads we have had on this forum where many interpretations, via decoherence, lead to that.

All he forgot to mention is its interpretation dependant.

Thanks
Bill

 

[TheScienceOrca]

No, it's more counterintuitive than that. The cat can only be in one state at a time, yes. But the states |ALIVE> and |DEAD> are *not* the only possible states the cat can be in, according to quantum theory. It can also be in a more general state that, mathematically, we would write as

|C> = a|ALIVE> + b|DEAD>

where a and b are complex numbers whose squared moduli add up to 1. (In general, a and b are time dependent; in the setup as Schrodinger originally gave it, a^2 decreases as time goes on, while b^2 increases). The point is that this general state |C> is a state which is a perfectly valid quantum state, according to the theory, but in which the cat is neither alive nor dead, nor is it correct to say that the cat "could" be alive or "could" be dead in this state. This state |C> that the cat is in during the experiment is simply a state that has no classical analogue, and no classical description like "cat alive" or "cat dead" or even "cat could be alive or could be dead".

We observe small objects like electrons in states like this all the time; but Schrodinger's point with the cat thought experiment was to raise the question of whether things like cats can really be in such states. (IIRC he thought they couldn't, and intended his thought experiment as a reductio ad absurdum of the claim that quantum mechanics was a complete theory.)

But the thing is regardless of whatever state you would like to call the cat it's either dead or alive in actuality.

If it's not then what is the arrangement of atoms (the cat) that is inside the box while no one is observing the cat.

If you are saying that is not there, then when you observer the now alive or dead cat where did this atoms come from that the observer now sees.

 

[bhobba]

But the thing is regardless of whatever state you would like to call the cat it's either dead or alive in actuality.

Absolutely.

The purpose of Schroedinger's Cat is to highlight an issue with Copenhagen.

In Copenhagen observations occur in an assumed classical world. For Schroedinger's Cat it's trivial - it happens at the particle detector - everything is classical from that point on - the cat is not in some kind of superposition - its alive or dead - period.

The issue is how does a theory that assumes the existence of a classical world explain that world. What is needed is a fully quantum theory of measurement, and Schroedinger's Cat shows the difficulty with trying to do that.

Since then a lot of work has been done on decoherence and much progress made - but a few issues remain.

Thanks
Bill

 

[nikkkom]

But the thing is regardless of whatever state you would like to call the cat it's either dead or alive in actuality.

That's the point: QM math is saying that the cat *can be* in a state of a mix (linear superposition, mathematically speaking) of a dead cat and a living cat. It's not that we don't know whether the cat is dead. QM says that he is neither. That's what equations are saying.

And yet, we see either a dead cat, or living cat. QM is fine with it: it says that observable states must be eigenstates. *Observed* cat can't be a linear superposition of eigenstates. *Observed* cat will be seen in one eigenstate. Dead. Or Living.

Which made people realize that the phrase "in actuality" is not as unambiguous as we thought. What is "actuality"? What word "exists" means? Or word "real"? What happens when we "observe"?

For example, a box with Schrodinger's cat can be put in a bigger box, with a scientist inside the bigger box. And we are on the outside. The scientist opens a smaller box. He will see either a living cat or a dead cat. But we, on the outside, don't know what he sees. For *us*, the scientist is *still* in a superposition of "I see dead cat" and "I see living cat" states.

 

[bhobba]

Which made people realize that the phrase "in actuality" is not as unambiguous as we thought. What is "actuality"? What word "exists" means? Or word "real"? What happens when we "observe"?

I think it made people realize we need a quantum theory of measurement rather than semantics.

For *us*, the scientist is *still* in a superposition of "I see dead cat" and "I see living cat" states.

Not so sure after decoherence that's the case.

Thanks
Bill

 

[phinds]

I think it made people realize we need a quantum theory of measurement rather than semantics.

Well said !

 

[PeterDonis]

regardless of whatever state you would like to call the cat it's either dead or alive in actuality.

This may be true; but if it's true, then quantum mechanics is incomplete.

If it's not then what is the arrangement of atoms (the cat) that is inside the box while no one is observing the cat.

The arrangement corresponding to the quantum state |C> = a|ALIVE> + b|DEAD>.

If you are saying that is not there

I'm not. Of course the atoms are "there"; the stuff inside the box has a quantum state. It's just not a quantum state that has any classical description.

Basically, you are claiming that anything that is "real" has to have a classical description. That may be true, but once again, *if* it's true, then quantum mechanics is incomplete, because quantum mechanics, as it stands, allows "real" things to be in states that have no classical description, like the state |C> above.

 

[PeterDonis]

Not so sure after decoherence that's the case.

Decoherence is what ensures that the only branches of the wave function that have nonzero amplitudes are the branches |ALIVE>|sees alive> and |DEAD>|sees dead>. In other words, decoherence is what ensures that there aren't any branches where the cat is alive but the observer sees a dead cat, or where the cat is dead but the observer sees a live cat.

But decoherence, by itself, can't explain why only one branch of the wave function "survives" the measurement: i.e., it can't explain why the final wave function of the whole system is either |ALIVE>|sees alive> *or* |DEAD>|sees dead>, as opposed to a|ALIVE>|sees alive> + b|DEAD>|sees dead>. The latter wave function is what you get when you just apply unitary evolution, i.e., without any collapse of the wave function. Decoherence doesn't collapse the wave function; so *if* it really is true that the final state of the whole system is either |ALIVE>|sees alive> *or* |DEAD>|sees dead>, and not a superposition of the two, then we need something more than just decoherence; we need a collapse. (This may be more or less what you meant when you said we need a quantum theory of measurement.)

 

[PeterDonis]

And yet, we see either a dead cat, or living cat. QM is fine with it: it says that observable states must be eigenstates. *Observed* cat can't be a linear superposition of eigenstates. *Observed* cat will be seen in one eigenstate. Dead. Or Living.

You left out a very important qualifier here: observable states must be eigenstates of the operator corresponding to the observable. So the reason we only observe cats that are alive or dead is that the physical process we use to observe cats realizes an operator that has |ALIVE> and |DEAD> as its eigenstates.

But it's perfectly possible in principle that there is some *other* physical process that we could use to interact with cats, which realizes an operator with different eigenstates, say (1/sqrt(2))(|ALIVE> + |DEAD>) and (1/sqrt(2))(|ALIVE> - |DEAD>). If we could construct a cat-observing device that realized this operator, then it would observe cats in what we ordinarily call superpositions of being alive and being dead. But with respect to this other operator, those states would *not* be superpositions; they would be eigenstates.

 

[nikkkom]

Decoherence is what ensures that the only branches of the wave function that have nonzero amplitudes are the branches |ALIVE>|sees alive> and |DEAD>|sees dead>. In other words, decoherence is what ensures that there aren't any branches where the cat is alive but the observer sees a dead cat, or where the cat is dead but the observer sees a live cat.

But decoherence, by itself, can't explain why only one branch of the wave function "survives" the measurement: i.e., it can't explain why the final wave function of the whole system is either |ALIVE>|sees alive> *or* |DEAD>|sees dead>, as opposed to a|ALIVE>|sees alive> + b|DEAD>|sees dead>.

At a risk of starting to build my own interpretation, I'd say that it's possible that the reality is a|ALIVE>|sees alive> + b|DEAD>|sees dead>.
QM has linear superpositions as a valid solutions exactly because parts of linear superposition do not "feel" each other.
The quantum system "you" which "sees a dead cat" can't know that there is also a quantum system "you" which "sees a living cat", and the full reality is a linear superposition of these.

A "Big box with (scientist and small box with cat)" situation seems to be easier to explain if we postulate that both versions of scientist are "real". We don't think that scientist sees a definite state of the cat *before* we ask the scientist what he sees, right?

 

[PeterDonis]

At a risk of starting to build my own interpretation, I'd say that it's possible that the reality is a|ALIVE>|sees alive> + b|DEAD>|sees dead>.

You don't need to build your own interpretation; this is just the MWI.

A "Big box with (scientist and small box with cat)" situation seems to be easier to explain if we postulate that both versions of scientist are "real".

If we are modeling the scientist and the cat as both being "in the box", and our asking the scientist what he sees is what "opens the box", then that just pushes the question up a level: how do we model *our* state on interacting with the scientist? Asking the scientist what he sees just puts *us* into a superposition of hearing the scientist respond "I see a live cat" and hearing the scientist respond "I see a dead cat". (At least, it does if you believe the MWI.)

 

[nikkkom]

While we are at it, can someone tell me which part of QM math says that observables are always eigenstates? This is a part which is less clear to me than the part where QM says that linear superpositions of solutions are solutions too.

 

[Nugatory]

While we are at it, can someone tell me which part of QM math says that observables are always eigenstates?

That's an axiom, one of the assumptions that we start with.

There was a thread not too long ago asking what motivated/justified this axiom; the motivation is that it leads to a very effective and useful theory that matches the way the world behaves.

 

[nikkkom]

That's an axiom, one of the assumptions that we start with.

Thanks.
The part of my question was, is there a mathematical formulation of this axiom?

You know, you can explain Dirac equation with English words, or you can just write i \hbar \gamma^\mu \partial_\mu \psi = m c \psi ...

 

[atyy]

While we are at it, can someone tell me which part of QM math says that observables are always eigenstates?

http://arxiv.org/abs/1007.4184 section 4.3.2, postulates 3 & 4
http://www.theory.caltech.edu/people/preskill/ph229/#lecture section 2.1, postulates 2 & 3

From the postulate of projective measurements, one can derive more general classes of measurements called POVMs. So some people prefer to use different axioms, making the POVMs fundamental rather than derived, eg.
http://arxiv.org/abs/1110.6815
http://arxiv.org/abs/0706.3526
http://arxiv.org/abs/0810.3536

 

[bhobba]

Decoherence is what ensures that the only branches of the wave function that have nonzero amplitudes are the branches |ALIVE>|sees alive> and |DEAD>|sees dead>.

I was referring to the statement about being in a superposition.

Superposition usually reefers to a complex linear combination of pure states giving other pure states. After decoherence we have a mixed state with suppressed off diagonal elements that's not generally viewed as a superposition.

Decoherence doesn't collapse the wave function; so *if* it really is true that the final state of the whole system is either |ALIVE>|sees alive> *or* |DEAD>|sees dead>, and not a superposition of the two, then we need something more than just decoherence; we need a collapse. (This may be more or less what you meant when you said we need a quantum theory of measurement.)

That's one of the issues I was referring to that still remain. The measurement problem has a number of parts. They all have been explained, except the most difficult one, the so called problem of outcomes, which is the modern variant of the collapse postulate (it not the same but is roughly similar - without detailing what 'roughly' means).

The solution to that problem requires some kind of additional assumption, the precise one used depending on interpretation.

Thanks
Bill

 

[bhobba]

While we are at it, can someone tell me which part of QM math says that observables are always eigenstates

I am not sure exactly what you mean by that.

You may mean for filtering type observations, the state after observation is an eigenstate of the observable.

The reason for that is just after the observation you would expect to get the same result if you did it again. When you chug through the math this means the state is an eigenstate of the observable.

The other thing you may be referring to is why are the outcomes mapped to a resolution of the identity.

I did a long post a while ago now explaining that one in detail (see post 137):
https://www.physicsforums.com/showthread.php?t=763139&page=8

Basically its a foundational axiom, even more basic than the concept of state.

The part of my question was, is there a mathematical formulation of this axiom?

Hopefully my link will explain exactly what the foundational assumption of QM is.

Thanks
Bill

 

[TheScienceOrca]

Doesn't seem to be very scientific reasoning, so because we can't predict the current state of the cat when then say the cat is in some new unique state?

What if there was someone standing behind you that you weren't aware of that had infrared goggles that could view if the cats heart had stopped or not.

He would know if the cat is dead or alive, but you would still declare it in some unique state.I think the root of the problem is that we aren't scientifically advanced enough to understand the current state of the radioactive material and the cat is just a way of understanding that easier as you can see an alive cat in your day to day life.

If we know how the radioactive material works (if it will give off radioactivity or not) then we know the state of the cat. The cat is either alive or dead and the moment the radioactive material is used, but since we don't understand how the radioactivity works fully we make the ASSUMPTION that the cat is neither live or dead.So the cat could be dead or could not be dead, directly relative to the state of the radioactive material.


So as you can see the cat is never dead and alive at the same time, the radio active material is simply unpredictable to our current knowledge. But because we don't know why this is happening I don't think we should make the claim it's random. That is like putting a bunch of cards in a hat and shaking it then when you take a card out claiming it's random.

The process is very NOT random, the card selected was the one that was moved by the card next to it that was bumped by another one and so forth. If you had a super computer you could easily predict it, but since the human without the super computer doesn't understand the process it assumes the process is random.

If that makes sense.

I know this is against the standard model, which by the way I am not arguing with I am just trying to get a better understanding.

 

[PeterDonis]

After decoherence we have a mixed state with suppressed off diagonal elements that's not generally viewed as a superposition.

But according to the MWI, it *is* a superposition (the mixed state is just an approximation). According to the MWI, unitary evolution is the only kind of evolution there is, and a unitary transformation can't turn a pure state into a mixed state.

(Bear in mind that I'm not necessarily agreeing with the MWI; I'm just trying to be clear about what it says.)

 

[PeterDonis]

If we know how the radioactive material works (if it will give off radioactivity or not) then we know the state of the cat.

But we don't know "how the radioactive material works", if by that you mean being able to predict exactly at what instant a given radioactive atom will decay. Furthermore, this is *not* a matter of there being internal "gears and wheels" inside the atom that we can't measure, that actually deterministically cause the atom to decay at some particular instant. In other words, it's *not* just a matter of us not knowing the exact state of the radioactive atom precisely enough.

The reason that isn't enough by itself is Bell's Theorem: no local hidden variable model can reproduce all the predictions of quantum mechanics. The model in which the atom has some internal "gears and wheels" that determine when it decays, and we just can't measure them precisely enough, is a local hidden variable model, so it can't reproduce all the predictions of quantum mechanics. So far, all experiments that have been done to test this have borne out the predictions of quantum mechanics: local hidden variable models are ruled out.

 

[TheScienceOrca]

But we don't know "how the radioactive material works", if by that you mean being able to predict exactly at what instant a given radioactive atom will decay. Furthermore, this is *not* a matter of there being internal "gears and wheels" inside the atom that we can't measure, that actually deterministically cause the atom to decay at some particular instant. In other words, it's *not* just a matter of us not knowing the exact state of the radioactive atom precisely enough.

The reason that isn't enough by itself is Bell's Theorem: no local hidden variable model can reproduce all the predictions of quantum mechanics. The model in which the atom has some internal "gears and wheels" that determine when it decays, and we just can't measure them precisely enough, is a local hidden variable model, so it can't reproduce all the predictions of quantum mechanics. So far, all experiments that have been done to test this have borne out the predictions of quantum mechanics: local hidden variable models are ruled out.

So as you stated in that second paragraph. The whole reason we don't know the state of the cat is because of our lack of understanding of the how the radioactive atom will decay which is not knowing how it works.

So the cat is never in some mysterious state, is simply dead or alive relative to the state of that atom, but since we don't know what the state of that atom the assumption is made the cat is neither dead or alive, but the cat is ALWAYS either died or alive. The only thing that I guess you could say is in a "limbo" state is the atom as it is neither radioactive or nonradioactive to our knowledge. This logic applies in a scenario where the geiger counter is out of the box as well and is visible. Before the experiment starts you know the cat is Alive. Once the experiment starts due to our lack of knowledge we don't know the state of the atom. But after x amount of time it takes for that radioactivity process ( I am unaware of the details ) to take place we will then know by viewing the Geiger counter the state of the atom and thus the state of the cat.




Perhaps in the future we will understand a new level of science within the atom that determines whether it's radioactive and this whole thing will be bunked, but ignore that previous statement to just stay on this current conversation.

 

[PeterDonis]

The whole reason we don't know the state of the cat

Who said we don't know the state of the cat? I said the exact opposite: we *do* know the state of the cat--it's just not a state that has a classical description.

is because of our lack of understanding of the how the radioactive atom will decay which is not knowing how it works.

You don't seem to be reading what I'm actually writing.

So the cat is never in some mysterious state, is simply dead or alive relative to the state of that atom

No, it isn't.

but since we don't know what the state of that atom

No, we *do* know the state of the atom, just as we do know the state of the cat--at least, we do according to standard QM. According to standard QM, the atom is in a superposition of being decayed and not being decayed; this is a perfectly definite quantum state--it just doesn't have a classical description. (And the only reason we describe this state as a superposition is relative to the "atom decay" operator. Relative to an operator that had the atom's state as an eigenstate, it would not be in a superposition.)

You appear to be misinterpreting a system being in a definite quantum state that doesn't have a classical description, as the system being in an unknown state. They are not the same.

 

[atyy]

But we don't know "how the radioactive material works", if by that you mean being able to predict exactly at what instant a given radioactive atom will decay. Furthermore, this is *not* a matter of there being internal "gears and wheels" inside the atom that we can't measure, that actually deterministically cause the atom to decay at some particular instant. In other words, it's *not* just a matter of us not knowing the exact state of the radioactive atom precisely enough.

The reason that isn't enough by itself is Bell's Theorem: no local hidden variable model can reproduce all the predictions of quantum mechanics. The model in which the atom has some internal "gears and wheels" that determine when it decays, and we just can't measure them precisely enough, is a local hidden variable model, so it can't reproduce all the predictions of quantum mechanics. So far, all experiments that have been done to test this have borne out the predictions of quantum mechanics: local hidden variable models are ruled out.

In the case of Schroedinger's cat, I don't think a Bell inequality is violated. So would it be possible that a future nonlocal hidden variable theory capable of explaining the violations of the Bell inequality, would reduce to a local hidden variable theory when considering Schroedinger's cat?

 

[PeterDonis]

In the case of Schroedinger's cat, I don't think a Bell inequality is violated.

Yes, I would agree, since there's only one "measurement" involved (the radioactive atom decaying).

So would it be possible that a future nonlocal hidden variable theory capable of explaining the violations of the Bell inequality, would reduce to a local hidden variable theory when considering Schroedinger's cat?

I suppose so, yes. But I don't think this is the argument that TheScienceOrca is making.

 

[TheScienceOrca]

Who said we don't know the state of the cat? I said the exact opposite: we *do* know the state of the cat--it's just not a state that has a classical description.



You don't seem to be reading what I'm actually writing.



No, it isn't.



No, we *do* know the state of the atom, just as we do know the state of the cat--at least, we do according to standard QM. According to standard QM, the atom is in a superposition of being decayed and not being decayed; this is a perfectly definite quantum state--it just doesn't have a classical description. (And the only reason we describe this state as a superposition is relative to the "atom decay" operator. Relative to an operator that had the atom's state as an eigenstate, it would not be in a superposition.)

You appear to be misinterpreting a system being in a definite quantum state that doesn't have a classical description, as the system being in an unknown state. They are not the same.

Ok, let me see if I understand what you are saying.

Do you believe in this experiment the state of the atom whichever you call it alive or dead or both at same time or however do you believe it is directly relative to the state of the cat?

 

[TheScienceOrca]

Yes, I would agree, since there's only one "measurement" involved (the radioactive atom decaying).



I suppose so, yes. But I don't think this is the argument that TheScienceOrca is making.

That is exactly what I am saying, for all we know, we have no clue how to measure those atoms and upon further advance in knowledge perhaps we will know what is going on, look back to my card in the hat analogy

 

[TheScienceOrca]

In addition to many more points/questions

 

[bhobba]

But according to the MWI, it *is* a superposition (the mixed state is just an approximation).

Sure. But it VERY quickly decays below our ability to detect.

Thanks
Bill

 

[bhobba]

Do you believe in this experiment the state of the atom whichever you call it alive or dead or both at same time or however do you believe it is directly relative to the state of the cat?

We know 100% for sure the cat is not in any kind of superposition that is detectable. In fact decoherence shows it decays to way way below our ability to detect very very quickly.

Thanks
Bill

 

[PeterDonis]

Do you believe in this experiment the state of the atom whichever you call it alive or dead or both at same time or however do you believe it is directly relative to the state of the cat?

The state of the system atom + cat looks like this:

a|atom intact>|cat alive> + b|atom decayed>|cat dead>

where the coefficients a and b are time-dependent (as I said before, a^2 decreases and b^2 increases as time passes), and a^2 + b^2 = 1.

This is a perfectly definite quantum state, but it does not have a classical description. It is *not* a state in which "we do not know" whether the atom is decayed or not decayed, or whether the cat is alive or dead.

 

[PeterDonis]

That is exactly what I am saying

Is it? It seems to me that you are saying that a theory of the kind you've been describing, where the only reason we can't predict exactly when a radioactive atom will decay is that we can't measure its properties accurately enough, can explain everything, and therefore it can explain the Schrodinger's cat experiment. But this amounts to saying that a local hidden variable theory can explain everything. It can't.

What atyy was saying is that a theory of the kind you've been describing *can't* explain everything; but it might turn out that a theory that *can* explain everything (which would *not* be a theory of the kind you've been describing), would have a theory of the kind you've been describing as a useful approximation for a case like the Schrodinger's cat experiment. (For what it's worth, I don't think that's very likely, but I can't say it isn't possible.)

 

[PeterDonis]

Sure. But it VERY quickly decays below our ability to detect.

But this is a limitation on our detection technology, not a limitation imposed by the laws of physics, correct? I.e., in principle there's nothing preventing us from eventually building a detection technology that *could* detect the superposition in this kind of scenario.

 

[nikkkom]

http://arxiv.org/abs/1007.4184 section 4.3.2, postulates 3 & 4
http://www.theory.caltech.edu/people/preskill/ph229/#lecture section 2.1, postulates 2 & 3

From the postulate of projective measurements, one can derive more general classes of measurements called POVMs. So some people prefer to use different axioms, making the POVMs fundamental rather than derived, eg.
http://arxiv.org/abs/1110.6815
http://arxiv.org/abs/0706.3526
http://arxiv.org/abs/0810.3536

Thanks, really helpful!

 

[bhobba]

But this is a limitation on our detection technology, not a limitation imposed by the laws of physics, correct?

Correct. But its used to explain the existence of the classical world that we generally interact with day to day unaided by technology. It happens so fast and goes to such a low level it's way below what can be detected even with the aid of our current most advanced technology, and certainly not unaided by it in everyday life.

In Schroedinger cat the thought experiment is not about someone who has some future technology (it may not even ever exist) that will allow them to detect not only the very quick decoherence of the cat but the decoherence that is going on around us all the time.

Thanks
Bill

 

[durant35]

Isn't it the case that the macroscopic object cannot be in a state of superposition in any instant if it isn't isolated? So decoherence happens at the particle detector and from that point on everything is classical, the cat evolves causally.

 

[bhobba]

Isn't it the case that the macroscopic object cannot be in a state of superposition in any instant if it isn't isolated? So decoherence happens at the particle detector and from that point on everything is classical, the cat evolves causally.

Yes - but the caveat is superposition of position.

This thread is so old I can't recall what I and others said - but I doubt I said anything to contradict that.

Thanks
Bill

 

[durant35]

But according to the MWI, it *is* a superposition (the mixed state is just an approximation). According to the MWI, unitary evolution is the only kind of evolution there is, and a unitary transformation can't turn a pure state into a mixed state.

(Bear in mind that I'm not necessarily agreeing with the MWI; I'm just trying to be clear about what it says.)

This is what PeterDonis said, that the mixed state is only an approximation. Is that only according to mwi? What does it mean for decoherence itself and the cat state?

 

[bhobba]

This is what PeterDonis said, that the mixed state is only an approximation. Is that only according to mwi? What does it mean for decoherence itself and the cat state?

Theoretically decoherence does not create an exact mixed state - but very very quickly is way way below detectability using current or any envisaged future technology. Some take this point to an extreme IMHO and claim its a big problem. IMHO it isn't, but there is no point in arguing it and I won't be drawn into it. IMHO it's how you approach applied areas where things are often like that. - they don't like things along the lines of for all practical purposes.

Thanks
Bill