Shrodinger's Cat Paradox: A Possible Solution

[Swapnil]

I am reading "Beyond Einstein" by Kaku and one quote in the book specially caught my attention.

... the superstring theory provides ... comprehensive way of looking at Schrodinder's cat. Usually, in quantum mechanics, physicists write the Schrodinger wave function of a certain particle. However, the complete quantum mechanical description of the superstring theory requires that we write the Schrodinger wave function of the entire universe... This does not resolve all the philosophical problems associated with Schrodinger's cat; it merely means that the original formulation of the problem ... may be incomplete.

Can't we give the same argument just by sticking to our present quantum theory? Why do we need to bring in superstring theory?

 

[StatMechGuy]

I am reading "Beyond Einstein" by Kaku and one quote in the book specially caught my attention.


Can't we give the same argument just by sticking to our present quantum theory? Why do we need to bring in superstring theory?

Because how else will the string theorists get grant money?

 

[Swapnil]

Because how else will the string theorists get grant money?

But seriously, why do they need to bring in Superstring theory?

 

[Epicurus]

But seriously, why do they need to bring in Superstring theory?

Just as Stat mech guy said, to get grant money. Superstring theory is a mathematical curiousity, it does not fulfil any of the requirements for a physical theory eg falsification. However I am betting they get funding from the usual physics sources.

I can't see any connection between schrodingers cat and string theory.

 

[zbyszek]

I am reading "Beyond Einstein" by Kaku and one quote in the book specially caught my attention.


Can't we give the same argument just by sticking to our present quantum theory? Why do we need to bring in superstring theory?

One can. Just elaborate which aspect of Schrodinger cat "paradox" would you like
to learn solution to.

 

[Swapnil]

One can. Just elaborate which aspect of Schrodinger cat "paradox" would you like
to learn solution to.

The aspect that the cat is neither dead nor alive until any measurement is made because the state of the uranium atom is "undefined" until any measurement is made.

 

[zbyszek]

The aspect that the cat is neither dead nor alive until any measurement is made because the state of the uranium atom is "undefined" until any measurement is made.

This is no paradox if you remmember that the "cat" in the sentence above means
an ensamble of identically prepared cats. Some of them will turn dead and the rest
-- alive.
The interesting part is if you can prove that in a single run of the cat experiment, i.e. with
one cat, the outcome is either dead or alive. Never a superposition: dead +/- alive.
This proof exists. If you are interested I can dwell on it.

Cheers!

 

[vanesch]

Never a superposition: dead +/- alive.
This proof exists. If you are interested I can dwell on it.

What stops you, in principle, from considering quantum cat interference experiments ?
Suppose - ok, this is jokingly of course - that the cat is standing on two bars before the experiment. When the cat is "dead" she'll fall in between the bars, and when the cat is live, she'll jump through a hole in a wall in front of her.

Now, imagine we have some "cat-reflector" on the floor of the box, which "shines" the (dead) cat also "through the hole" where she is supposed to be jumping through when she's alive. This will then create an interference pattern between the "dead cat beam" (onto the floor, and the cat reflector, through the hole) and the "live cat beam" (directly through the hole), and so there should be maxima for the |dead>+|live> state which correspond to minima for the |dead>-|live> state and vice versa.
So looking at the position of our cat after the hole, we would measure, not a "live" cat, or a "dead" cat, but rather, a live+dead cat or a live-dead cat.

 

[zbyszek]

What stops you, in principle, from considering quantum cat interference experiments ?
Suppose - ok, this is jokingly of course - that the cat is standing on two bars before the experiment. When the cat is "dead" she'll fall in between the bars, and when the cat is live, she'll jump through a hole in a wall in front of her.

Now, imagine we have some "cat-reflector" on the floor of the box, which "shines" the (dead) cat also "through the hole" where she is supposed to be jumping through when she's alive. This will then create an interference pattern between the "dead cat beam" (onto the floor, and the cat reflector, through the hole) and the "live cat beam" (directly through the hole), and so there should be maxima for the |dead>+|live> state which correspond to minima for the |dead>-|live> state and vice versa.
So looking at the position of our cat after the hole, we would measure, not a "live" cat, or a "dead" cat, but rather, a live+dead cat or a live-dead cat.

O.K. Suppose the cat is in a alive+dead state. To simplify problem let's assume
for a moment that cat consists of N identical bosons. N is large.
The state alive+dead we can write as |N,0> + |0,N>, namely as the bosonic Schrodinger
cat state, where first slot corresponds to a single particle wave function w0(x) and the second slot to w1(x).
For all we know, to generate an outcome of a single measurement on the state we
draw one point (positions of all N particles) from 3N dimensional probability density
given by the N-body wave function modulus squared.

It turns out that this probability density for large N has two SEPARATE nonzero sectors:
one for |N,0> and one for |0,N>. I you draw just one point out of it, the point will
belong to one of the sectors. The cat turns to either alive or dead in the single run.

Similar in spirit argument works for fermions and distiguishible particles. You don't
have to believe my words. You can check the calculations yourself. They are available
through arXives.


Cheers!

 

[ZapperZ]

This is no paradox if you remmember that the "cat" in the sentence above means
an ensamble of identically prepared cats. Some of them will turn dead and the rest
-- alive.
The interesting part is if you can prove that in a single run of the cat experiment, i.e. with
one cat, the outcome is either dead or alive. Never a superposition: dead +/- alive.
This proof exists. If you are interested I can dwell on it.

Cheers!

But again (as in previous discussion on this issue), you're ignoring the fact that there ARE consequences of the dead and alive superposition. The coherence gap measured in Delft/Stony Brook experiments clearly is one such example. The situation of either dead or alive will NOT produce such consequences.

Zz.

 

[Schrodinger's Dog]

Just as Stat mech guy said, to get grant money. Superstring theory is a mathematical curiousity, it does not fulfil any of the requirements for a physical theory eg falsification. However I am betting they get funding from the usual physics sources.

I can't see any connection between schrodingers cat and string theory.

What are the usual suspects? And why are they so keen to fund something that is non falsifiable, and thus could ultimately be of no practical use? Are they banking on the experimental proof turning up or is there some other motivation, what do they know that we don't? Or are some institutions being lead up the garden path?

 

[zbyszek]

But again (as in previous discussion on this issue), you're ignoring the fact that there ARE consequences of the dead and alive superposition. The coherence gap measured in Delft/Stony Brook experiments clearly is one such example. The situation of either dead or alive will NOT produce such consequences.

Zz.

Of course there are consequences! The Shroedinger cat state is fully coherent (i.e. pure
, as oposite to mixed) with its all ability to interfere and so on. As any other quantum state that is pure. More, this state can never be classical, no matter how macroscopic
it is. Even if you know the state exactly you can only guess what a measurement will reveal in a single run. Whereas with classical object when you know its "classical state"
(positions + velocities), you know exactly the measurement outcome.

However, when you sample the corresponding probability density for a Schrodinger cat state to generate a single measurement outcome, you get only cat dead or alive. Nothing in between.

Cheers!

 

[vanesch]

However, when you sample the corresponding probability density for a Schrodinger cat state to generate a single measurement outcome, you get only cat dead or alive. Nothing in between.

No. The point is (as Zapper on a more serious note said), if the pure state with the quantum cat, the cat mirror and the hole is |live> + |dead> cat, then, if you repeat this experiment a 1000 times, you will find your cat only in certain positions, and never in others (interference fringes in cat position).

While if you only had a probability density "live" (50%) and "dead" (50%), you would find your cat uniformly distributed in position: no interference fringes in cat position.

Note: of course there's a problem with entanglement with internal degrees of freedom, for a genuinly dead or live cat (that is, its internal state is different, and entangled with its "trajectory"). So it would be necessary to insert a "cat ressurection device" in the falling cat beam, or a cat killing device in the direct beam, to erase the difference in internal states, so that they can factor out and allow for a pure position interference), so that the livelyness of the cat, after "interference" is not an indication of which path information.

 

[vanesch]

What are the usual suspects? And why are they so keen to fund something that is non falsifiable, and thus could ultimately be of no practical use?

Fame, promise, hope, dreams and,... derived products (like books for the general public, t-shirts and TV-appearance).

 

[ZapperZ]

Of course there are consequences! The Shroedinger cat state is fully coherent (i.e. pure
, as oposite to mixed) with its all ability to interfere and so on. As any other quantum state that is pure. More, this state can never be classical, no matter how macroscopic
it is. Even if you know the state exactly you can only guess what a measurement will reveal in a single run. Whereas with classical object when you know its "classical state"
(positions + velocities), you know exactly the measurement outcome.

However, when you sample the corresponding probability density for a Schrodinger cat state to generate a single measurement outcome, you get only cat dead or alive. Nothing in between.

Cheers!

I don't believe so. In fact, based on what understood from the formulation based on Tony Leggett's paper[1], there WILL be a difference between (i) superposition of states of the single cat, measured repeatedly versus (ii) a many dead cats and many alive cats, measured one at a time many times. The coherence energy gap measured in those SQUID experiments can be obtained from a single measurement, in principle, and will only occur if there is a superposition of the direction of the supercurrent current flow. In a superconducting state, the whole supercurrent is a single entity, i.e. it is not "many cats".

Zz.

[1] A.J. Leggett, J. Phys. Condens. Matt., v.14, p.415 (2002).

 

[zbyszek]

No. The point is (as Zapper on a more serious note said), if the pure state with the quantum cat, the cat mirror and the hole is |live> + |dead> cat, then, if you repeat this experiment a 1000 times, you will find your cat only in certain positions, and never in others (interference fringes in cat position).

While if you only had a probability density "live" (50%) and "dead" (50%), you would find your cat uniformly distributed in position: no interference fringes in cat position.

Note: of course there's a problem with entanglement with internal degrees of freedom, for a genuinly dead or live cat (that is, its internal state is different, and entangled with its "trajectory"). So it would be necessary to insert a "cat ressurection device" in the falling cat beam, or a cat killing device in the direct beam, to erase the difference in internal states, so that they can factor out and allow for a pure position interference), so that the livelyness of the cat, after "interference" is not an indication of which path information.

Could you, please, write the state that undergoes the measurement? For simplicity, suppouse that we start with a bosonic Schrodinger cat state: |N,0> + |0,N>,
if it is not a problem. What happens with it after the mirror, the hole ,etc? The final state,
please.

Cheers!

 

[Careful]

I don't believe so. In fact, based on what understood from the formulation based on Tony Leggett's paper[1], there WILL be a difference between (i) superposition of states of the single cat, measured repeatedly versus (ii) a many dead cats and many alive cats, measured one at a time many times. The coherence energy gap measured in those SQUID experiments can be obtained from a single measurement, in principle, and will only occur if there is a superposition of the direction of the supercurrent current flow. In a superconducting state, the whole supercurrent is a single entity, i.e. it is not "many cats".

Zz.

[1] A.J. Leggett, J. Phys. Condens. Matt., v.14, p.415 (2002).

You are right, but in this case I did not find such superposition to be strange : as I seem to remember from the paper (some time ago) it was about two supercurrents going in opposite directions through a tube connected by a Josephson bridge. The whole difficulty with superposition manifests itself when measuring superpositions of product states. In the latter paper, ``measurement'' was not causing a reduction of the state (a point the authors should have payed more attention to from the QM perspective, albeit it is intuitively clear).

 

[zbyszek]

I don't believe so. In fact, based on what understood from the formulation based on Tony Leggett's paper[1], there WILL be a difference between (i) superposition of states of the single cat, measured repeatedly versus (ii) a many dead cats and many alive cats, measured one at a time many times. The coherence energy gap measured in those SQUID experiments can be obtained from a single measurement, in principle, and will only occur if there is a superposition of the direction of the supercurrent current flow. In a superconducting state, the whole supercurrent is a single entity, i.e. it is not "many cats".

I agree on your points (i) and (ii). There is difference! I didn't considered (ii) so far
on this forum. I was only concerned with (i)-- a pure Schrodinger cat state. Still the
mathematical structure of the corresponding probability density is such that in a single
measurement you will get almost certainly cat dead or cat alive. The more particles
involved the greater the certainty.

A superconducting state represents many identically prepared superconductors.
Somtimes however (BCS superconductor, BEC, ...) a single quantum object
consisting of many particles gives the same averages (when averaged over all particles)
as an ensemble of single quantum objects. A member of an ensemble has the same
properties as the ensemble itself.

In these cases you can really apply QM to a single quantum object! But this is only in the
large N limit and for very special quantum states.

Cheers!

 

[ZapperZ]

You are right, but in this case I did not find such superposition to be strange : as I seem to remember from the paper (some time ago) it was about two supercurrents going in opposite directions through a tube connected by a Josephson bridge. The whole difficulty with superposition manifests itself when measuring superpositions of product states. In the latter paper, ``measurement'' was not causing a reduction of the state (a point the authors should have payed more attention to from the QM perspective, albeit it is intuitively clear).

But having two currents going in opposite direction isn't the case here. If it were, then there's nothing unusual about this experiment and the results would never get into a journal like Nature.

If we buy the QM description of superconductivity, then the supercurrent is a single, coherent entity. It is this single entity that has two different directions of transport. The state description isn't composed of a percentage of the supercurrent having one direction, while the rest goes the other way. The description is one in which the supercurrent has both directions, and the ratio of the probability of one versus the other depends on the external magnetic field. The predicted outcome of the same measurement will not produce the same results if you simply have two independent currents going in opposite directions.

Zz.

 

[ZapperZ]

I agree on your points (i) and (ii). There is difference! I didn't considered (ii) so far
on this forum. I was only concerned with (i)-- a pure Schrodinger cat state. Still the
mathematical structure of the corresponding probability density is such that in a single
measurement you will get almost certainly cat dead or cat alive. The more particles
involved the greater the certainty.

I don't think there's any argument here in terms of the outcome of a measurement that measures one or the other. However, I'm arguing about the fact that the superposition does create a series of testable consequences. If by opening the box you make a measurement of the dead or alive characteristics of the cat, then don't open the box and measure an operator that is non-commuting to "opening the box". This would not cause the state to choose one over the other and thus, the superposition is maintained. It is this measurement that I'm focusing on, and it is this measurement that has been done in those two experiments that I cited. They didn't measure if the supercurrent is moving one way or the other because the very act of such a measurement will give then only one answer. Instead, they measure the consequence of such a superposition by measuring the energy spectrum instead. The existence of the coherent energy gap is consistent with the superposition of states and not simply a matter of having a current going one way or the other.

The very same principle also explains the bonding-antibonding bands we have in solid state physics and chemistry. An electron residing in only one of the bands would not cause an interference with itself from the other band to cause the presence of bonding and antibonding states. It must be in a superposition of both bands for that to occur.

Zz.

 

[Careful]

But having two currents going in opposite direction isn't the case here. If it were, then there's nothing unusual about this experiment and the results would never get into a journal like Nature.

If we buy the QM description of superconductivity, then the supercurrent is a single, coherent entity. Zz.

Well clearly, I don't buy that and that is why on a personal note, I said I did not find it strange. One could imagine two superwaves going in opposite directions, interfering with one another. If one supercurrent is a wave, then two currents going in opposite directions are expected to interfere. I know it is not the standard way of looking at it, but alas, the latter does not make sense at all.

Careful

 

[vanesch]

Could you, please, write the state that undergoes the measurement? For simplicity, suppouse that we start with a bosonic Schrodinger cat state: |N,0> + |0,N>,
if it is not a problem. What happens with it after the mirror, the hole ,etc? The final state,
please.

Ok, here we go.

We represent the cat state by a cartesian product:
the internal state of the particles |N,0> "cat dead" and |0,N> "cat live", and the center of gravity of the cat |position>

The cat state |psi1> = |N,0> |cat_ready_position> + |0,N>|cat_ready_position>

The "cat falls through the bars or jumps" is represented by the evolution operator U1.

U1 |N,0> |cat_ready_position> = |N,0> |cat_through_hole>


U1 |0,N> = |0,N> |cat_on_mirror>

so |psi2> = U1 |psi1> = |N,0>|cat_through_hole> + |0,N>|cat_on_mirror>

Next, we consider the "cat killing device" which is needed to avoid entanglement with internal degrees of freedom. It is placed in the "cat_trhough_hole" path, and hence leaves other cats unaffected.
This is the "which path" erasure, because the "which path" information was included in the state of life of the cat.

U2 |N,0> |cat_through_hole> = |0,N> |cat_through_hole>
U2 |any> |other position> = |any> |other position>

|psi3> = U2 |psi2> = |0,N> |cat_through_hole> + |0,N> |cat_on_mirror>

Next, we consider propagation of the cat position states, and the action of the mirror, which reflects the cat also through the hole. Of course, because of unitarity, this cannot result in exactly the same state of |cat_through_hole>. There will be a slight inclination between the 2 cat beams, given by the angles th1 and th2 for resp. the "direct" cat beam, and the "cat beam from the mirror".
So we now have:
U3 |any> |cat_through_hole> = |any> exp(i k1 z cos th1) blob(x,y)
U3 |any> |cat_on_mirror> = |any> exp(i k1 z cos th2) blob(x,y)

So |psi4> = U3 |psi3>
= |0,N> ( exp(i k1 z cos th1) + exp(i k1 z cos th2) ) blob(x,y)

A measurement at z = (2n + 1) pi / (k1 cos[th1] - k1 cos[th2]) will yield no cat, while near z = (2n ) pi / (k1 cos[th1] - k1 cos[th2])
we will find cat peaks.

All cats will be in the |0,N> internal state (dead).

If we started out with just a statistical mixture of dead and live cats, we would get a uniform distribution of dead cats along z for the same setup.

 

[ZapperZ]

Well clearly, I don't buy that and that is why on a personal note, I said I did not find it strange. One could imagine two superwaves going in opposite directions, interfering with one another. If one supercurrent is a wave, then two currents going in opposite directions are expected to interfere. I know it is not the standard way of looking at it, but alas, the latter does not make sense at all.

Careful

It makes sense to me because the standard way to describe superconductivity has passed a huge amount of verification. I've long ago concluded that my "sense" can often be wrong, and experimental observation trumps "sense" every single time.

BTW two separate supercurrents going in opposite directions would not interfere coherently, i.e. you would not get the fraunhoffer pattern that you'd get out of a SQUID. There's no reason for them keep the exact same phase difference with each other over many measurements.

Zz.

 

[zbyszek]

I don't think there's any argument here in terms of the outcome of a measurement that measures one or the other. However, I'm arguing about the fact that the superposition does create a series of testable consequences.

Dear ZapperZ,

1. Could you be so kind and read again the Swapnil's question and my answer to it?
Is my answer wrong or incomplete in a way that justifies your accusation of me ignoring something?

2. Do you find me denying anywhere that "the superposition does create a series of testable consequences"?

Cheers!

 

[Careful]

BTW two separate supercurrents going in opposite directions would not interfere coherently, i.e. you would not get the fraunhoffer pattern that you'd get out of a SQUID. There's no reason for them keep the exact same phase difference with each other over many measurements.

Zz.

Well, here you make the extra assumption that the two currents would be independent, I never claimed they were. On the contrary, this is clearly a coherent phenomenon, but that doesn't imply I cannot speak of separate identities within the latter. Anyway, that's all I wanted to point out (I am not discussing the status of QM).

Careful

 

[ZapperZ]

Dear ZapperZ,

1. Could you be so kind and read again the Swapnil's question and my answer to it?
Is my answer wrong or incomplete in a way that justifies your accusation of me ignoring something?

2. Do you find me denying anywhere that "the superposition does create a series of testable consequences"?

Cheers!

Sure, this one:

This is no paradox if you remmember that the "cat" in the sentence above means
an ensamble of identically prepared cats. Some of them will turn dead and the rest
-- alive.
The interesting part is if you can prove that in a single run of the cat experiment, i.e. with
one cat, the outcome is either dead or alive. Never a superposition: dead +/- alive.
This proof exists. If you are interested I can dwell on it.

I believe I have been trying to show that there is a difference between "dead and alive" versus "dead or alive", and that the former is what is detected in the experiments that I cited.

Zz.

 

[ZapperZ]

Well, here you make the extra assumption that the two currents would be independent, I never claimed they were. On the contrary, this is clearly a coherent phenomenon, but that doesn't imply I cannot speak of separate identities within the latter. Anyway, that's all I wanted to point out (I am not discussing the status of QM).

Careful

But by assuming that they are not independent, then you're making an assumption that somehow, they know just the right amount of phase difference to maintain each and every time, and for different experiments (eg. Josephson current in tunneling). Considering your objection towards QM, don't you think equally makes no "sense"?

Zz.

 

[zbyszek]

Ok, here we go.

We represent the cat state by a cartesian product:
the internal state of the particles |N,0> "cat dead" and |0,N> "cat live", and the center of gravity of the cat |position>

The cat state |psi1> = |N,0> |cat_ready_position> + |0,N>|cat_ready_position>

The "cat falls through the bars or jumps" is represented by the evolution operator U1.

U1 |N,0> |cat_ready_position> = |N,0> |cat_through_hole>


U1 |0,N> = |0,N> |cat_on_mirror>

so |psi2> = U1 |psi1> = |N,0>|cat_through_hole> + |0,N>|cat_on_mirror>

Next, we consider the "cat killing device" which is needed to avoid entanglement with internal degrees of freedom. It is placed in the "cat_trhough_hole" path, and hence leaves other cats unaffected.
This is the "which path" erasure, because the "which path" information was included in the state of life of the cat.

U2 |N,0> |cat_through_hole> = |0,N> |cat_through_hole>
U2 |any> |other position> = |any> |other position>

|psi3> = U2 |psi2> = |0,N> |cat_through_hole> + |0,N> |cat_on_mirror>

Next, we consider propagation of the cat position states, and the action of the mirror, which reflects the cat also through the hole. Of course, because of unitarity, this cannot result in exactly the same state of |cat_through_hole>. There will be a slight inclination between the 2 cat beams, given by the angles th1 and th2 for resp. the "direct" cat beam, and the "cat beam from the mirror".
So we now have:
U3 |any> |cat_through_hole> = |any> exp(i k1 z cos th1) blob(x,y)
U3 |any> |cat_on_mirror> = |any> exp(i k1 z cos th2) blob(x,y)

So |psi4> = U3 |psi3>
= |0,N> ( exp(i k1 z cos th1) + exp(i k1 z cos th2) ) blob(x,y)

A measurement at z = (2n + 1) pi / (k1 cos[th1] - k1 cos[th2]) will yield no cat, while near z = (2n ) pi / (k1 cos[th1] - k1 cos[th2])
we will find cat peaks.

All cats will be in the |0,N> internal state (dead).

If we started out with just a statistical mixture of dead and live cats, we would get a uniform distribution of dead cats along z for the same setup.

Thank you!

The state |psi4> isn't a Schrodinger cat state, so you are not talking about measurement
on SCS. Your claim is the same as ZapperZ's that one can do things to a superposition
that won't flight with mixtures. I agree.

My point, on the other hand, is that if you perform a position measurement on |N,0> + |0,N> then you will see no difference between this and the mixture: |N,0> with prob. 1/2 and |0,N> with prob. 1/2, provided N is large enough.


Cheers!

 

[Careful]

But by assuming that they are not independent, then you're making an assumption that somehow, they know just the right amount of phase difference to maintain each and every time, and for different experiments (eg. Josephson current in tunneling). Considering your objection towards QM, don't you think equally makes no "sense"?

Zz.

Well, as far as I remember, this phase difference is determined by the local physics at the Josephson bridge. Moreover, it only needs to be maintained on the average, and that doesn't seem weird to me at all. Anyway, first things first.

Careful

 

[ZapperZ]

Well, as far as I remember, this phase difference is determined by the local physics at the Josephson bridge. Moreover, it only needs to be maintained on the average, and that doesn't seem weird to me at all. Anyway, first things first.

Careful

I'm not sure what you mean exactly here. The only thing that the junction (if that is what you meant by "bridge") affects on the josephson current is the current amplitide, not the phase, via the Ambegaokar-Baratoff relationship.

In any case, there has to be something that correlate the two currents. What would this be?

Zz.

 

[Careful]

I'm not sure what you mean exactly here. The only thing that the junction (if that is what you meant by "bridge") affects on the josephson current is the current amplitide, not the phase, via the Ambegaokar-Baratoff relationship.

In any case, there has to be something that correlate the two currents. What would this be?

Zz.

I quickly glanced upon the Leggett paper, in particular formulae 5.22, 5.23 which give the eigenstates for an effective Hamiltonian in which cooper pairs can tunnel through the (bridge) junction (a so called classically forbidden phenomenon). The latter states, expressed in the eigenstates of the Hamiltonian in which tunneling is forbidden depend upon a tunneling amplitude and the energy of the latter. Personally, I do not know what is ``strange'' about this (there is nothing weird about tunneling).

Careful

 

[ZapperZ]

I quickly glanced upon the Leggett paper, in particular formulae 5.22, 5.23 which give the eigenstates for an effective Hamiltonian in which cooper pairs can tunnel through the (bridge) junction (a so called classically forbidden phenomenon). The latter states, expressed in the eigenstates of the Hamiltonian in which tunneling is forbidden depend upon a tunneling amplitude and the energy of the latter. Personally, I do not know what is ``strange'' about this (there is nothing weird about tunneling).

Careful

My reference to tunneling was for the generic field. In tunneling spectroscopy in particular, for a superconductor-insulator-superconductor junction, you get what is known as the Josephson current whereby at zero bias, a spontaneous current flows in BOTH directions. We (I) see this in the I-V curve of the tunnel junction. If you look at the state describing this, it is really a superposition of currents in both directions, not separate currents in both directions. A clear effect of this is on how the probability of each direction can shift depending on from which direction you approach zero bias.

So the very same principle is also at work in a totally different experiment than the SQUID experiment.

Zz.

 

[vanesch]

My point, on the other hand, is that if you perform a position measurement on |N,0> + |0,N> then you will see no difference between this and the mixture: |N,0> with prob. 1/2 and |0,N> with prob. 1/2, provided N is large enough.

Of course, for a given measurement basis, you cannot distinguish between a pure state and the corresponding mixture.
So, it is necessary to change measurement basis in order to even hope to find a difference between the pure state and the mixture.

 

[Careful]

My reference to tunneling was for the generic field. In tunneling spectroscopy in particular, for a superconductor-insulator-superconductor junction, you get what is known as the Josephson current whereby at zero bias, a spontaneous current flows in BOTH directions. We (I) see this in the I-V curve of the tunnel junction. If you look at the state describing this, it is really a superposition of currents in both directions, not separate currents in both directions. A clear effect of this is on how the probability of each direction can shift depending on from which direction you approach zero bias.

So the very same principle is also at work in a totally different experiment than the SQUID experiment.

Zz.

I do not follow now : I acknowledged there is a superposition of currents in both directions, we simply do not agree whether this is a mysterious superposition of two states of one current or two separate (correlated) interfering currents, that's all.

 

[demo001]

This experiment is fataly floored.
you will never find an alive cat this is why.
quantum superposition
In the experiment Shrodinger explains that the qubit is in quantum superposition however it then goes on to ignore the simple fact that in superposition the qubit is in all states at once.
He goes on to explain correctly we will not know what state it will come to rest in until we open the box.
Nothing radical there is there?
However the simple fact ignored is in the superposition state of the qubit and the fact that the switch is looking for just one state a state that the superpositioned qubit will always exibit when inside the box before opened. Therefore the gas is always released long before the box is ever opened the cat can never be alive.
The only way a cat could ever be alive would be if the qubit was never in superposition in the first place in which case the experiment failed before it starts.
At best this experiment can only prove superposition eg the case of the cat being dead but the qubit when observed not being in the correct state to have triggerd the switch.