Is Schrodinger's cat experiment a paradox?

[rede96]

I have no background in quantum physics (or any physics really) its just a topic I find really interesting.

I watched a video on schrodinger's cat and am struggling to understand the cat being in a state of superposition. In the thought experiment I saw there was an radioactive atom with a half life of one hour in a box with a geiger counter connected to some poison. And of course the cat. It was explained that statically there was a 50/50 chance the atom would decay but of course according to the Copenhagen interoperation it was until you opened the box that you would find out if the cat was alive or dead and until the point the cat existed in both states.

What I was wondering is why couldn't they just put a timer on the Geiger counter, which started the moment the experiment was started. Once the lid was lifted, say 90 minutes after the start of the experiment, and if the cat was found dead, then they could have just checked the time counter to see when the atom decayed. If it was say after 60 minutes then doesn't that sort of suggest that cat didn't exist in both states before the box was opened?

Or am I missing something?

 

[ChrisVer]

Schrodinger's cat experiment tells you that you cannot determine the system's state until you somehow interact/observe it.
On the other hand you cannot know whether the cat is dead or alive in that experiment's set-up. As you said,in your suggestion, you had again to open the box and see the cat is dead. Before that though, you only knew the chances were 50-50. What if the cat was still alive let us say?

Also, I am kind of skeptic on the timer thing- it can play the role of an observer.

 

[phinds]

I think Schrodinger really came up with the cat thing to show how silly the Copenhagen interpretation can be.

Personally, I'm really confident that the moon is there whether I'm looking at it or not and I think the cat is always either alive or dead.

 

[rede96]

Schrodinger's cat experiment tells you that you cannot determine the system's state until you somehow interact/observe it.
On the other hand you cannot know whether the cat is dead or alive in that experiment's set-up. As you said,in your suggestion, you had again to open the box and see the cat is dead. Before that though, you only knew the chances were 50-50. What if the cat was still alive let us say?

Also, I am kind of skeptic on the timer thing- it can play the role of an observer.

The point was in my suggestion that yes I did have to open the box to find out if the cat was dead but if I checked the timer and found the atom decayed before I opened the box I would know the cat was dead before I opened the box. So it wasn't opening the box that determined the outcome. Which was in contradiction to what was being said.

Of course if the cat was alive I'd just repeat the experiment, but at some point I would find the cat dead.

 

[phinds]

The point was in my suggestion that yes I did have to open the box to find out if the cat was dead but if I checked the timer and found the atom decayed before I opened the box I would know the cat was dead before I opened the box. So it wasn't opening the box that determined the outcome. Which was in contradiction to what was being said.

Of course if the cat was alive I'd just repeat the experiment, but at some point I would find the cat dead.

I think you are missing the point here that the Copenhagen interpretation does not require a PERSON to make the observation. If you have a mechanism that operates a timer based on the decay, THAT is an observation and according to Copenhagen the cat was both alive and dead up until the mechanism observed the decay and turned off the timer. That is, your solution has not avoided the problem with the Copenhagen interpretation.

 

[ChrisVer]

I think you are missing the point here that the Copenhagen interpretation does not require a PERSON to make the observation.

That was the main thing...when I posted about the "experiment's set-up" I meant exactly the set-up of Schodinger's experiment. The observation is done by the timer...

 

[Catflap]

It was a joke.

But it illustrates a basic concept. Any interaction between particles represents an 'observation'. The world proceeds between interactions in a state of uncertainty, which is resolved when the result of the interaction 'happens'.

It was probably the worst joke in the history of science. There's nothing less funny than a joke that has to be explained over and over and over and over...and even then, few people ever 'get' it.

 

[ChrisVer]

It was a joke.

But it illustrates a basic concept. Any interaction between particles represents an 'observation'. The world proceeds between interactions in a state of uncertainty, which is resolved when the result of the interaction 'happens'.

It was probably the worst joke in the history of science. There's nothing less funny than a joke that has to be explained over and over and over and over...and even then, few people ever 'get' it.

Of course a few people get it. The problem with that experiment is that it considers a classical object (a cat) and people are quiet unfamiliar of thinking an \frac{1}{\sqrt{2}} [ |alive> \pm |dead> ] cat...
However in QM objects this illustration seems plausible, and once you understand the QM illustration you can somehow imagine the cat's thing...

 

[phinds]

That was the main thing...when I posted about the "experiment's set-up" I meant exactly the set-up of Schodinger's experiment. The observation is done by the timer...

But your OP said that you had solved the problem of the superposition of the cat. MY point was that you did not. Your scenario still has the cat in superposition, it just changes the timing of when the superposition ends from when the person opens the box to back when the timer stopped.

OOPS ... I've confused your posts with the OP's post. My apologies.

 

[Maui]

Quantum mechanics isn't a complete description of reality. You can't really hope to explain 'cats' or derive the conflict at the Maidan in Kiev with the formalism.

 

[rede96]

I think you are missing the point here that the Copenhagen interpretation does not require a PERSON to make the observation. If you have a mechanism that operates a timer based on the decay, THAT is an observation and according to Copenhagen the cat was both alive and dead up until the mechanism observed the decay and turned off the timer. That is, your solution has not avoided the problem with the Copenhagen interpretation.

I understand that the outcome can't be predetermined but I am struggling to get my head around how the cat can exist in two states.

Maybe its just the thought experiment that is confusing me, as I could have done the same thing with a glass box and watched the whole thing unfold. During the process I wouldn't have seen two cats, one alive and one dead. I would have just seen the Geiger counter trigger, the poison release and the cat die.

The other thing that confuses me is if I watched the whole thing unfold, does that mean I predetermined the outcome?

All very confusing!

But thanks for your time.

 

[phinds]

I understand that the outcome can't be predetermined but I am struggling to get my head around how the cat can exist in two states.

Maybe its just the thought experiment that is confusing me, as I could have done the same thing with a glass box and watched the whole thing unfold. During the process I wouldn't have seen two cats, one alive and one dead. I would have just seen the Geiger counter trigger, the poison release and the cat die.

The other thing that confuses me is if I watched the whole thing unfold, does that mean I predetermined the outcome?

All very confusing!

But thanks for your time.

You are missing the point of the replies. The cat does NOT exist in two states, that just a Copenhagen interpretation of the formal math of QM and Schrodinger's POINT was to illustrate that fact.


Also, according to even Copenhagen, much less common sense, if you watched there would be no "paradox" or superposition because the system would be under constant observation.

 

[WannabeNewton]

Quantum mechanics isn't a complete description of reality. You can't really hope to explain 'cats' or derive the conflict at the Maidan in Kiev with the formalism.

This. The formalism in and of itself doesn't explain physically the transition that happens between unitary time evolution of the state of the system under the Schrodinger equation and the projection onto an element of a preferred basis upon measurement.

 

[phinds]

This. The formalism in and of itself doesn't explain physically the transition that happens between unitary time evolution of the state of the system under the Schrodinger equation and the projection onto a preferred basis upon measurement.

Can you say that in English?

 

[Maui]

Can you say that in English?

He is saying what I said in the quote in a technical way - i.e. you need additional assumptions to get outcomes and... errr...yes- atoms, molecules, cats, etc.

 

[ChrisVer]

I understand that the outcome can't be predetermined but I am struggling to get my head around how the cat can exist in two states.

Maybe its just the thought experiment that is confusing me, as I could have done the same thing with a glass box and watched the whole thing unfold. During the process I wouldn't have seen two cats, one alive and one dead. I would have just seen the Geiger counter trigger, the poison release and the cat die.

The other thing that confuses me is if I watched the whole thing unfold, does that mean I predetermined the outcome?

All very confusing!

But thanks for your time.

What you need to understand it, is kind of classical. For example think about a box with gas inside. You cannot determine the state (eg speed) of a molecule in the gas, except for if you measure it. You can speak about possible outcomes (distributions).
The main difference between that classical view (statistical mechanics) and the quantum mechanics, is that the statistics in classical physics come out of undetermined parameters (eg initial state) and our incapability of watching out the motion of billions of bodies... The same thing happens with the dice, you can drop the dice and it will bring an outcome with 1:6 possibility (depends on the dice structure). In that case you would be able to determine every outcome if you knew all needed parameters (eg initial position, velocity, geometry of the dice etc). However statistically, you could say that dropping a dice you have 1/6 possibility of it coming out 1, 1/6 for coming out 2 etc (so it's in a superposition)
In QM , the possibilities, and so the superposition, are intrinsic and cannot be determined by any unknown parameters (Bell's experiment proved that). And according to Cop. School, which I think is closest even to the modern view, you cannot determine the outcome of an observation (dropping of dice) except for if you observe it. So observing the whole procedure let us say through a glass box, you would have immediately made the superposition to collapse in one state (cat: dead, cat :alive - no need for being 50-50 alive/dead)

 

[bahamagreen]

It is kind of a joke; the additional assumptions must include that the cat has been properly prepared so ensure that it is living the ninth of its nine lives when placed in the box.

 

[ChrisVer]

It is kind of a joke; the additional assumptions must include that the cat has been properly prepared so ensure that it is living the ninth of its nine lives when placed in the box.

Isn't the cat itself an observer? in its reference frame, the collapse happens before our own... so does the reference frames play a role?

 

[bhobba]

I think Schrodinger really came up with the cat thing to show how silly the Copenhagen interpretation can be. Personally, I'm really confident that the moon is there whether I'm looking at it or not and I think the cat is always either alive or dead.

That's true - but the devil is in the detail of exactly in what way it showed it was silly.

According to Copenhagen there is a commonsense classical world out there and QM is a theory about observations that occur in that world.

In Schrodinger's cat the observation is at the particle detector, everything is commonsense classical from that point on - the cat is never alive and dead - it is alive or dead - period.

So what was its purpose? It bought to light the REAL issue with QM. Since its a theory about observations in an assumed classical world, and since that classical world is in fact composed of quantum objects how does such a theory explain it? In other words we need a fully quantum theory of measurement without this arbitrary classical cut. What Schrodinger's Cat showed is if you try that problems arise.

However since then a lot of work has been done, particularly in the area of decoherence, on developing such a fully quantum theory of measurement and how a classical world arises. Significant progress has been made, but some issues remain and research is ongoing.

The moon is there when you are not looking because it is being observed all the time by its environment. A few stray photons from the CMBR is enough to decohere a dust particle and give it a definite position. The moon its much larger and the number of photons it interacts with is so large its there regardless - no question.

Thanks
Bill

 

[bhobba]

Isn't the cat itself an observer? in its reference frame, the collapse happens before our own... so does the reference frames play a role?

You guys are all missing the point of the thought experiment.

Schrodinger's Cat is utterly trivial in Copenhagen.

Copenhagen assumed the existence of a commonsense classical world observations appear in. The observation occurred at the particle detector - everything is classical from that point on. The cat is alive or dead - period.

Its real purpose was to show we need a fully quantum theory of measurement.

Maybe Weinberg can explain it better (see the section on Contra Quantum Mechanics):
http://scitation.aip.org/content/aip/magazine/physicstoday/article/58/11/10.1063/1.2155755
'Bohr’s version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wavefunction (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?'

Scrodinger's Cat was simply a demonstration of the above. Since then a lot of work has been done fixing that issue.

There also seems to be possibly some confusion about exactly what Copenhagen says. Check out:
http://motls.blogspot.com.au/2011/05/copenhagen-interpretation-of-quantum.html

Thanks
Bill

 

[StevieTNZ]

The moon is there when you are not looking because it is being observed all the time by its environment. A few stray photons from the CMBR is enough to decohere a dust particle and give it a definite position. The moon its much larger and the number of photons it interacts with is so large its there regardless - no question.

I would question that. The photons from the CMBR would simply entangle with the dust particle, thus giving rise to superposition of states of positions, in principle.

 

[Ryan McCarty]

rede96, I believe your confusion lies in the fact that you are trying to view this from a physical point of view. Erwin Schrodinger developed this thought experiment to show problems with the Copenhagen interpretation of QM. One of those is that superposition cannot be imagined in a physical sense. Likewise, your thought experiment cannot be imagined in one either. That is, unless you use something other than the Copenhagen interpretation of QM. If you you use another interpretation like Hugh Everett's Many-Worlds interpretation than you can view it in a physical sense - sort of anyways. Imagine it as the cat exists in a state of "Dead" in world one world and "Alive" in another. Until the cat has been observed, both worlds exist in equal potential of possibility. It is only when you observe the cat that one scenario is defined and you know which occurs in your reality. If the cat was in a glass box you would not see both a "Dead" cat and an "Alive" cat as there is only one scenario in your specific reality and the two scenarios exist in different realities. Thus, there is only one outcome in your reality. And, there would be no uncertainty as you would know your specific scenario because you would observe it instantly through the glass.

 

[bhobba]

I would question that. The photons from the CMBR would simply entangle with the dust particle, thus giving rise to superposition of states of positions, in principle.

Decoherence is a form of entanglement. It causes the off diagonal elements of the state to vanish leading to apparent, effective, whatever term you want to use, collapse:
http://www.ipod.org.uk/reality/reality_decoherence.asp
'The off-diagonal (imaginary) terms have a completely unknown relative phase factor which must be averaged over during any calculation since it is different for each separate measurement (each particle in the ensemble). As the phase of these terms is not correlated (not coherent) the sums cancel out to zero. The matrix becomes diagonalised (all off-diagonal terms become zero). Interference effects vanish. The quantum state of the ensemble system is then apparently "forced" into one of the diagonal eigenstates with the probability of a particular eigenstate selection predicted by the value of the corresponding diagonal element of the density matrix.'

Thanks
Bill

 

[Jilang]

A great link Bill.

 

[ChrisVer]

about the last link, could someone give an actual example for a mixed and pure state? Because I'm having some confusion in understanding the difference...
does it say that a particle could be described by a:
pure state
|Ψ>= \frac{1}{\sqrt{2}} [ |0> \pm |1> ]
while in mixed each can have either 0 or 1?
|Ψ>= |0> or |Ψ>= |1>

 

[rede96]

rede96, I believe your confusion lies in the fact that you are trying to view this from a physical point of view. Erwin Schrodinger developed this thought experiment to show problems with the Copenhagen interpretation of QM. One of those is that superposition cannot be imagined in a physical sense. Likewise, your thought experiment cannot be imagined in one either.

Yes, I guess I was trying to see how all this strangeness actually manifested itself in the macro world.

But what is driving that is trying to understand that the outcome of something, say the time for an atomic atom to decay, is never known until its observed. It sounds like that is the same as saying if a tree falls in the woods and no one hears it does it make a sound?

My response to that would be of course it does make a 'sound'. The physics of a tree falling isn't dependant on someone being around to hear it. Which is the same as saying the physics of anything that happens in the real world isn't dependant on something being able to observe it.

So that is sort of what I was thinking about. I know making an observation can effect the result (e.g. the double slit experiment) but if I find it hard to comprehend that if I didn't make the observation, that some result wouldn't have just happened anyway. AND, if it were possible to repeat the exact same conditions then the result would be exactly the same.

But it does seem from my limited knowledge of QM that it may be impossible to re-recreate a set of conditions at the quantum level. At least by design.

That is, unless you use something other than the Copenhagen interpretation of QM. If you you use another interpretation like Hugh Everett's Many-Worlds interpretation than you can view it in a physical sense - sort of anyways. Imagine it as the cat exists in a state of "Dead" in world one world and "Alive" in another. Until the cat has been observed, both worlds exist in equal potential of possibility. It is only when you observe the cat that one scenario is defined and you know which occurs in your reality. If the cat was in a glass box you would not see both a "Dead" cat and an "Alive" cat as there is only one scenario in your specific reality and the two scenarios exist in different realities. Thus, there is only one outcome in your reality. And, there would be no uncertainty as you would know your specific scenario because you would observe it instantly through the glass.

Again I know too little about QM to make any valid feedback but find it really hard to believe that there are 'many worlds' and only through observation does one of those world occur in reality.

 

[ChrisVer]

Again, in QM you cannot know the results of an observation before doing it.
For example you have a machine that creates electrons in general (spin-1/2 particles). You make them pass through a magnetic field. Then you would see their trajectory separated, indicating different spin orientations, which would imply that the electrons coming from your canon would have spin up or spin down (they exist in such a state). The magnetic field though separates them- makes them distinguishable (you will have spin up going one way, spin down going the other way).
But before applying the magnetic field, you wouldn't be able to distinguish which electrons have spin up or spin down...

am I wrong?

However, if the electrons interacted among themselves or the canon shooting them, I don't know how could someone interpret the Stern-Gerlachs' experiment. Of course 10^{7} sec,as stated in the previous article, for electrons(microscopic particles) would be enough to conduct the experiment without problem

 

[Jilang]

Chris, it's deeper than that. They didn't have a defined spin when they left the cannon. The choice of the magnetic field direction in your experiment effectively quantises the spin in that direction.

 

[ChrisVer]

Chris, it's deeper than that. They didn't have a defined spin when they left the cannon. The choice of the magnetic field direction in your experiment effectively quantises the spin in that direction.

I don't disagree, they are practically in a superposition of spin up & down...

 

[rede96]

Chris, it's deeper than that. They didn't have a defined spin when they left the cannon. The choice of the magnetic field direction in your experiment effectively quantises the spin in that direction.

Sorry for the stupid question but how do we know they didn't have a defined spin when they left the cannon if the measurements system we use to detect the spin will effect the result?

 

[Jilang]

Because Bells Inequalities are violated in QM ruling out hidden variables. Look up Bells Theorum.

 

[Ryan McCarty]

It sounds like that is the same as saying if a tree falls in the woods and no one hears it does it make a sound?

This is more of a philosophical question with no definite answers. It all depends on how you define existence and it is seemingly impossible to prove anyone solution. I tend to lead more towards the idea that an observer is not needed to "define" a reality but only to conclude a specific reality's existence. The tree always falls, it's just that we don't know in which reality it falls until we observe the fall. Until we do this, their is equal potential that in our reality the the tree falls and does not fall.

Which is the same as saying the physics of anything that happens in the real world isn't dependant on something being able to observe it.

Again, the physics of your reality exist regardless of an observer. But, you do not know which occurs until you observe which actually occurs. Of course, something may exist before you observe it, but consciousness is needed to conclude what occurs.

Again I know too little about QM to make any valid feedback but find it really hard to believe that there are 'many worlds' and only through observation does one of those world occur in reality.

In 'many worlds' all realities occur simultaneously, it's just that you exist in only one reality and therefore there is only one outcome in your reality. This outcome exists in superposition because your reality could be infinitely many until you "discover" which one it actually is. We call this discovery "observing" because the only way to discover the outcome is to consciously observe it.

Also, it may help to remember to think in paradoxes. Humans evolved to experience the world in a limited way. Because we do not live on a quantum scale our sense's, our mind's, have great trouble understanding QM. Just because things occur in definite ways on your scale doesn't mean quantum particles occur the same way.

Hopefully this helps:thumbs:

 

[Maui]

As the phase of these terms is not correlated (not coherent) the sums cancel out to zero.

This is assumed, right? And it is the environment that causes the phases to shift out of coherence and this purported environment is somehow 'classical'. Sorry but if i understand this correctly, you are talking about religion, not science and if this is the progress you allude to, we are in the middle of nowhere with no hope whatsoever of an adequate solution to the MP.

 

[rede96]

This is more of a philosophical question with no definite answers. It all depends on how you define existence and it is seemingly impossible to prove anyone solution. I tend to lead more towards the idea that an observer is not needed to "define" a reality but only to conclude a specific reality's existence. The tree always falls, it's just that we don't know in which reality it falls until we observe the fall. Until we do this, their is equal potential that in our reality the the tree falls and does not fall.

Personally I don't see this as a philosophical problem. The tree falls, it hits the ground creating sound waves which propagate through the air at the speed of sound. I agree that if I don't hear or see the tree fall then I will never know if it has or not. And that there is a chance the tree I am thinking of may have fallen or may not. But we don't need multiple realities for that?

Again, the physics of your reality exist regardless of an observer. But, you do not know which occurs until you observe which actually occurs. Of course, something may exist before you observe it, but consciousness is needed to conclude what occurs.

I wasn't too sure what you meant by that to be honest.

In 'many worlds' all realities occur simultaneously, it's just that you exist in only one reality and therefore there is only one outcome in your reality. This outcome exists in superposition because your reality could be infinitely many until you "discover" which one it actually is. We call this discovery "observing" because the only way to discover the outcome is to consciously observe it.

Also, it may help to remember to think in paradoxes. Humans evolved to experience the world in a limited way. Because we do not live on a quantum scale our sense's, our mind's, have great trouble understanding QM. Just because things occur in definite ways on your scale doesn't mean quantum particles occur the same way.

Hopefully this helps:thumbs:

I appreciate the help, but I just don't get the many worlds theory. At the quantum level I guess that there aren't too many outcomes possible from a decaying atom, but at the macro level I find it difficult to think that nature would know every single possible outcome from an event and how it effects the total system, and they all exists simultaneously until one is observed.

I think I need to be a bit more reading :D

 

[WannabeNewton]

about the last link, could someone give an actual example for a mixed and pure state?

Mixed states are classical ensembles just like in statistical mechanics. They will necessarily be convex combinations of pure states. Pure states represent a complete knowledge of a given system whereas mixed states represent ignorance about the system and the probabilities given by the trace of mixed state operators represent true ignorance again just like in statistical mechanics. Therefore it's important not to confuse convex combinations of pure states with superpositions of pure states-the probabilities associated with the latter cannot be interpreted in terms of ignorance and represent a departure from classical ensembles.

 

[WannabeNewton]

Sorry for the stupid question but how do we know they didn't have a defined spin when they left the cannon if the measurements system we use to detect the spin will effect the result?

You need to first understand QM before delving into the foundations. It seems like you're still confusing the lack of knowledge about a system until a measurement reveals what the state of the system was all along with superposition in the context of QM. The latter cannot be interpret in that classical way! If we did interpret superpositions in that way then we would run into a contradiction when time-evolving a system backwards using the Schrodinger equation.

 

[Jilang]

This is assumed, right? And it is the environment that causes the phases to shift out of coherence and this purported environment is somehow 'classical'. Sorry but if i understand this correctly, you are talking about religion, not science and if this is the progress you allude to, we are in the middle of nowhere with no hope whatsoever of an adequate solution to the MP.

Decoherence is not a religion and there is no Measurement Problem according to this:
http://physics.about.com/od/quantumphysics/fl/Decoherence-and-the-Measurement-Problem.htm
There is no clear dividing line between the quantum and classical world, just the interference effects become much less noticeable in the latter.

 

[Maui]

Decoherence is not a religion and there is no Measurement Problem according to this:
http://physics.about.com/od/quantumphysics/fl/Decoherence-and-the-Measurement-Problem.htm
There is no clear dividing line between the quantum and classical world, just the interference effects become much less noticeable in the latter.

Did you read your own link? It says the same things i outlined in my previous post. How could that be legitimate science?

" As the phase angles lose their coherence through interaction with the surrounding environment, the result is classical probability and the absence of quantum behavior, which means that traditional methods of analyzing the situation using classical physics techniques is a valid approximation."How is that science instead of bad philosophy(aka religion)?BTW, one should maintain a truly sceptical position anytime someone makes a statement that the MP has been resolved, esp. if no Nobel Prizes had been awarded.

 

[WannabeNewton]

Decoherence is not a religion and there is no Measurement Problem according to this...

Decoherence doesn't solve the measurement problem. That's not even the intent of the decoherence program. You shouldn't use "About.com" as a resource, just sayin'

 

[Jilang]

What is the decoherence program and what are its intentions? It sounds kinda sinister!

 

[Maui]

What is the decoherence program and what are its intentions? It sounds kinda sinister!

To attempt to identify the mechanism that decoheres coherent states.

Its primary aim seems to be to somehow, if possible, engage the 'environment', the measuring apparatus and a global wavefunction of the world. In the end, if enough people accept their assumptions, establish the idea among peers that collapse of the wavefunction is unnecessary.

Just my impressions from reading this board.

 

[WannabeNewton]

What is the decoherence program and what are its intentions? It sounds kinda sinister!

Isn't all of this sinister in the end?

Read p.6 of this paper: http://arxiv.org/pdf/1402.1217.pdf

 

[DrewD]

This is assumed, right? And it is the environment that causes the phases to shift out of coherence and this purported environment is somehow 'classical'. Sorry but if i understand this correctly, you are talking about religion, not science and if this is the progress you allude to, we are in the middle of nowhere with no hope whatsoever of an adequate solution to the MP.

Decoherence is not a solution to the measurement problem, but you can easily prove to yourself that it happens with a simple computer program. The environment is not "classical", just large compared to the system being measured. Decoherence definitely happens, the question is how general and how important it is. It seems to "solve" the measurement problem for larger systems (it takes a quantum statistical problem and turns it into a "classical" statistical problem), but when individual particles are concerned, it is unclear. Why should we see just one eigenvalue? There still must be a measurement postulate.

 

[Maui]

It seems to "solve" the measurement problem for larger systems (it takes a quantum statistical problem and turns it into a "classical" statistical problem)

How? You should not assume the Born rule to be able to derive decoherence as it leads to the idea of priviliged decohering chairs, apparatues, etc. Namely, what you intend to prove is already there. It's injecting classicality to derive classicality. Doesn't sound very convincing, does it?

 

[bhobba]

about the last link, could someone give an actual example for a mixed and pure state? Because I'm having some confusion in understanding the difference...
does it say that a particle could be described by a:
pure state
|Ψ>= \frac{1}{\sqrt{2}} [ |0> \pm |1> ]
while in mixed each can have either 0 or 1?
|Ψ>= |0> or |Ψ>= |1>

The issue is states are not elements of a vector space as some books, especially those at the intermediate level like Griffiths, will tell you. They are in fact positive operators of unit trace defined by the general form of the Born Rule. To really grasp it you need to see the two axioms of QM as detailed by Ballentine in his text.

1. To each observation there corresponds a Hermitian operator whose eigenvalues give the possible outcomes of the observation.
2. There exists a positive operator of unit trace P such that the expected outcome of the observation associated with the observable O is E(O) = Trace (PO) - this is the Born Rule in its most general form. By definition P is called the state of the system.

In fact the Born Rule is not entirely independent of the first axiom, as to a large extent it is implied from that via Gleason's Theroem - but that would take us too far afield - I simply mention it in passing.

Also note that the state, just like probabilities, is simply an aid in calculating expected outcomes. Its not real like say an electric field etc. In some interpretations its real - but the formalism of QM is quite clear - its simply, like probabilities, an aid in calculation.

By definition states of the form |x><x| are called pure. States that are a convex sum of pure states are called mixed ie are of the form ∑ pi |xi><xi| where the pi a positive and sum to one. It can be shown all states are either pure or mixed. Applying the Born rule to mixed states shows that if you have an observation whose eigenvectors are the |xi><xi| then outcome |xi><xi| will occur with probability pi. Physically one can interpret this as a system in state |xi><xi| randomly presented for observation with probability pi. In such a case no collapse occurs and an observation reveals what's there prior to observation - many issues with QM are removed. Such states are called proper mixed states.

Pure states, being defined by a single element of a vector space, can be associated with those elements and that's what's usually done. Of course when you do that they obey the vector space properties so the principle of superposition holds ie if |x1> and |x2> are any two pure states a linear combination is also a pure state. This is what is meant by a superposition. Note it deals with elements of a vector space not convex sums of pure states when considered operators - they are mixed states. This means the state 1/2 |x1> + 1/2 |x2> is a pure state and is totally different from the mixed state 1/2 |x1><x1| + 1/2 |x2><x2|.

Now what decoherence does is transform a superposition like 1/2 |x1> + 1/2 |x2> into a mixed state like 1/2 |x1><x1| + 1/2 |x2><x2|. When that is done it can be interpreted as a proper mixed state which solves many of the issues with collapse etc.

Hope this helps.

Thanks
Bill

 

[bhobba]

This is assumed, right? And it is the environment that causes the phases to shift out of coherence and this purported environment is somehow 'classical'. Sorry but if i understand this correctly, you are talking about religion, not science and if this is the progress you allude to, we are in the middle of nowhere with no hope whatsoever of an adequate solution to the MP.

Of course its an assumption. Randomly pick objects and they have a random properties - its almost (but not quite) the definition of randomly picking. Its made all the time by actuaries, statisticians, engineers, applied mathematicians etc etc. It really is utterly trivial, and if invalid we are really up shite creek without a paddle, not just in QM but many many areas.

But still, yes its an assumption, but one you are scraping the bottom of the barrel to doubt IMHO. The desperation some are driven to to hold certain views in QM never ceases to amaze me.

Thanks
Bill

 

[bhobba]

I wasn't too sure what you meant by that to be honest.

I am pretty sure he is just presenting the Many Worlds take on it.

Mathematically its a very very beautiful interpretation, utterly beguiling and breathtaking in its elegance and simplicity. I like it very very much and even got David Wallices textbook on it:
https://www.amazon.com/dp/0199546967/?tag=pfamazon01-20

Suffice to say its not my preferred interpretation, but really such things as deciding between interpretations without experimental support is philosophy, which, correctly IMHO, is off topic here. We can discuss interpretations, and explain them, but philosophically dissecting them is better suited to a philosophy forum, not one like this devoted to physics.

So I will simply say - selecting a preferred interpretation without experimental support is an opinion - opinions are like bums - everyone has one - it doesn't make it correct.

Thanks
Bill

 

[Maui]

Of course its an assumption. Randomly pick objects and they have a random properties - its almost (but not quite) the definition of randomly picking. Its made all the time by actuaries, statisticians, engineers, applied mathematicians etc etc. It really is utterly trivial, and if invalid we are really up shite creek without a paddle, not just in QM but many many areas.

But still, yes its an assumption, but one you are scraping the bottom of the barrel to doubt IMHO. The desperation some are driven to to hold certain views in QM never ceases to amaze me.

Thanks
Bill

I do not see the justification for splitting the world into classical and quantum and you have not provided one. If you need a classical world to get decoherence, why would you need decoherence at all? You'd already have a classical world of environments, apparatueses, tables and chairs... there is nothing to explain.

It really is utterly trivial, and if invalid we are really up shite creek without a paddle, not just in QM but many many areas.

Are we not?

 

[bhobba]

Decoherence is not a religion and there is no Measurement Problem according to this:
http://physics.about.com/od/quantumphysics/fl/Decoherence-and-the-Measurement-Problem.htm

Decoherence is most definitely NOT a religion.

But without reading the link I can assure you there is a measurement problem even with decoherence.

First you need to understand what the measurement problem is. Its not really the collapse issue you read about because most of the time the system is destroyed by measurement. What it really is is basically understanding what the dickens is going on with the Born rule. It has a number of parts, such as the preferred basis problem and probably the toughest one of all - why do we get any outcomes at all. There are others as well - if you want to go deeply into it get Schlosshauer's textbook:
https://www.amazon.com/dp/3642071422/?tag=pfamazon01-20

Now decoherence definitely explains some parts of the measurement problem, probably other parts such as the preferred basis problem (but further research is required to be sure), however it is powerless to explain why we get any outcomes at all. Its trivial in Many Worlds, Bohmian Mechanics etc - but the formalism of QM by itself simply says - you get outcomes.

Then there are unresolved issues like the so called factoring problem.

There is no clear dividing line between the quantum and classical world, just the interference effects become much less noticeable in the latter.

That's true - but that in itself creates issues.

Decoherence has made great strides in allowing us to understand the emergence of a classical world, and in formulating a fully quantum theory of measurement - but issues still remain - although of course research is ongoing.

Thanks
Bill

 

[bhobba]

I do not see the justification for splitting the world into classical and quantum and you have not provided one.

But I don't do that, nor does dechorence do that.

In fact that's the big advantage of decoherence - it avoids that, and allows you to define a measurement as after decoherence - nothing classical at all.

The measurement problem is still there for reasons I stated in my previous post. It has enough issues without giving it problems it doesn't have.

Thanks
Bill