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Is "Schrodinger's Cat" the wrong interpretation for Copenhagen Interpretation?

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11 hours ago, swansont said:

It's irrelevant to the problem. You can write down states of an atom or nucleus and represent it as a superposition. There isn't anything absurd about that. It's chosen because it's random.

Are you suggesting that a cat cannot be in superposition because the states are too complex to be written down?

 

11 hours ago, swansont said:

t spoils the party if it does something to affect the phonon state in that example. Not all interactions will cause decoherence.

From wikipedia:

Quote

A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue. 

That seems to imply decoherence does not spoil the superposition.

 

11 hours ago, swansont said:

Happens all the time. Superposition and its removal is integral to how an atomic clock works. When we detect photons coming from our atoms, we know what transition they've made, and what state they are in.

That does not exclude the possibility that instead of these atoms going to a certain state, we as observers got entangled with the atoms.

 

11 hours ago, swansont said:

The thing about interpretation is that they either make sense, or they don't (or they are somewhere on a spectrum between the two). There's a subjective element — it's whether they make sense to you. Because that's the function of an interpretation: to help you understand what's going on in the QM. It's like a toy model, and you use what works.

So, the Copenhagen interpretation is the right model to use if it helps you understand the example. The many-worlds interpretation is the right model to use if it helps you understand the example. Shut-up-and-calculate is the right model to use if it helps you understand the example.

Exactly.

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12 hours ago, Bender said:

Are you suggesting that a cat cannot be in superposition because the states are too complex to be written down?

It is not clear that life or death is dependent on a set of configurations of quantum states. AFAIK it doesn't boil down to life being an electron that's spin up or down, and death being the opposite.

Quote

From wikipedia:

That seems to imply decoherence does not spoil the superposition.

We aren't talking about a global wavefunction in that example. It's a single state.

Quote

That does not exclude the possibility that instead of these atoms going to a certain state, we as observers got entangled with the atoms.

As with something I said before, it makes no sense to say two things got entangled without specifying what quantum state is entangled.

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8 hours ago, swansont said:

It is not clear that life or death is dependent on a set of configurations of quantum states. AFAIK it doesn't boil down to life being an electron that's spin up or down, and death being the opposite.

Every interaction between the possible decay of the isotope and the opening of the box that has more than one outcome with a nonzero probability, causes the decoherence of superimposed quantum states (not sure whether I worded that 100% correctly, but I'm confident you get what I mean). I see no reason why you can't combine all those superpositions to one gargantuan state space.

Someone referred to engineering where usually lots of modes/states/loads can be superimposed.

 

8 hours ago, swansont said:

We aren't talking about a global wavefunction in that example. It's a single state.

I guess I was. I did suggest that the entire planet could get entangled with the cat. Moreover, Schrodingers cat only makes sense in a global wavefunction. 

I didn't know the term, though.

8 hours ago, swansont said:

As with something I said before, it makes no sense to say two things got entangled without specifying what quantum state is entangled. 

Irrelevant : yes; pointless: certainly; but why does it make no sense?

Edited by Bender

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On ‎4‎/‎17‎/‎2018 at 11:18 AM, swansont said:

The thing about interpretation is that they either make sense, or they don't (or they are somewhere on a spectrum between the two). There's a subjective element — it's whether they make sense to you. Because that's the function of an interpretation: to help you understand what's going on in the QM. It's like a toy model, and you use what works.

So, the Copenhagen interpretation is the right model to use if it helps you understand the example. The many-worlds interpretation is the right model to use if it helps you understand the example. Shut-up-and-calculate is the right model to use if it helps you understand the example.

 

 

With respect, that's sitting on the fence, not an answer to the OP.

 

The interpretation in question is the Copenhagen Interpretation. The cat is a proposed example of the use/application of that interpretation, stated by its author as intended to show the limits if not the flakiness of Copenhagen.

 

Given that how can Copenhagen help understand the supplied example?

 

The obvious conclusion is that Copenhagen is inadequate to explain/describe all instances of quantum behaviour.

 

As to the basis, Copenhagen is founded on superposition.

I think the example requires HUP. Otherwise why is it impossible to know the state? such a restriction does not appear in Copenhagen & superposition itself.

 

There are further issues which I was considering developing in a separate thread, if anyone is interested.

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12 minutes ago, studiot said:

With respect, that's sitting on the fence, not an answer to the OP.

Or it's saying the answer is subjective, so don't think you are getting any objective answer that's valid.

12 minutes ago, studiot said:

The interpretation in question is the Copenhagen Interpretation. The cat is a proposed example of the use/application of that interpretation, stated by its author as intended to show the limits if not the flakiness of Copenhagen.

But it also depends on extending QM well beyond where QM is the proper description of the physics.

12 minutes ago, studiot said:

Given that how can Copenhagen help understand the supplied example?

 

The obvious conclusion is that Copenhagen is inadequate to explain/describe all instances of quantum behaviour.

Here's the problem. In quantum physics, you can come up with experiments where a superposition allows for an interference of states, and the Copenhagen interpretation would seem to excel at explaining this. And I don't think many-worlds does (at least, I can't think of any examples off the top of my head). So all one has to do is come up with some kind of Schrödinger's cat interferometer

12 minutes ago, studiot said:

 

As to the basis, Copenhagen is founded on superposition.

I think the example requires HUP. Otherwise why is it impossible to know the state? such a restriction does not appear in Copenhagen & superposition itself.

What conjugate variables are being measured simultaneously?

 

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2 minutes ago, swansont said:

Or it's saying the answer is subjective, so don't think you are getting any objective answer that's valid.

 

 

A subjective answer in Science?

3 minutes ago, swansont said:

 

But it also depends on extending QM well beyond where QM is the proper description of the physics.

 

 

Yes agreed, which I why I am suggesting a spin off thread, without the OP question to answer.

3 minutes ago, swansont said:

.

Here's the problem. In quantum physics, you can come up with experiments where a superposition allows for an interference of states, and the Copenhagen interpretation would seem to excel at explaining this. And I don't think many-worlds does (at least, I can't think of any examples off the top of my head). So all one has to do is come up with some kind of Schrödinger's cat interferometer

 

 

That was the whole point of my posted article from Dr Gribben (who put it so well  thought). We do not have a single explanation/model that covers all bases.

But trying to understand something in terms of a mdoel which does not cover the base in point is futile.

3 minutes ago, swansont said:

What conjugate variables are being measured simultaneously?

 

I didn't say there were, I said it was claimed to be impossible to know if the radioactive nucleus had decayed.

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2 hours ago, Bender said:

Every interaction between the possible decay of the isotope and the opening of the box that has more than one outcome with a nonzero probability, causes the decoherence of superimposed quantum states (not sure whether I worded that 100% correctly, but I'm confident you get what I mean). I see no reason why you can't combine all those superpositions to one gargantuan state space.

Given what studiot just posted, it makes more sense to look at it your way: all of the QM is tied up in the event that gives you the random outcome. Forget the cat; it's a distraction.

Quote

 I guess I was. I did suggest that the entire planet could get entangled with the cat. Moreover, Schrodingers cat only makes sense in a global wavefunction. 

That exchange was about the entangled diamonds. But it's a phonon state, so it's a particular vibrational mode that's entangled.

Quote

I didn't know the term, though.

Irrelevant : yes; pointless: certainly; but why does it make no sense?

Because of what entanglement is and how it's defined. It lacks critical information. To use a favorite analogy, it's like asking, "What's the difference between a duck?"

8 minutes ago, studiot said:

A subjective answer in Science?

Is a QM interpretation science?

 

Quote

I didn't say there were, I said it was claimed to be impossible to know if the radioactive nucleus had decayed.

How does that involve the HUP?

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44 minutes ago, swansont said:

Here's the problem. In quantum physics, you can come up with experiments where a superposition allows for an interference of states, and the Copenhagen interpretation would seem to excel at explaining this. And I don't think many-worlds does (at least, I can't think of any examples off the top of my head).

That's a matter of taste. Copenhagen doesn't explain anything that many-worlds can't. It is just a different approach. I would even argue that Copenhagen raises additional questions, such as the mechanism behind the "wavefunction collapse" or the line between the quantum world and the macroscopic world.

Does the superposition of the phonon eg collapse when a particle interacts with it, or only when that particle interacts with something else afterwards?

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1 hour ago, Bender said:

Copenhagen doesn't explain anything that many-worlds can't. It is just a different approach

How does many worlds explain superposed phenomena in this world, for instance chemical bonding?

Superposition is not a feature of many worlds, it is a feature of Copenhagen.

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5 hours ago, studiot said:

How does many worlds explain superposed phenomena in this world, for instance chemical bonding?

Superposition is not a feature of many worlds, it is a feature of Copenhagen.

How can superposition not feature in many-worlds? The thing with many-worlds is that everything remains in superposition.

To me, the only difference between the two is how decoherence is explained: either by collapse or by the observer "joining" the superposition. 

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3 hours ago, Bender said:

The thing with many-worlds is that everything remains in superposition.

 

Superposition refers to states not things. I believe swansont has already mentioned this.

 

3 hours ago, Bender said:

How can superposition not feature in many-worlds?

 

The point about many worlds is that most of the states do not exist in our world. Hence the many worlds label.

These states always exist, regardless of event in our world. So there is no collapse to a particular state.

Superposition (as in Engineering) requires all the states to exist together, as they do in my example of molecular bonding.

Have you heard of the LCAO method in Chemistry? (Linear combination of atomic orbitals) It is the simplest attempt to derive bonding from the states of individual atoms by superposition.

 

 

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8 hours ago, studiot said:

Superposition refers to states not things. I believe swansont has already mentioned this.

Tomato tomato. How about "Everything stays in superimposed states".

 

8 hours ago, studiot said:

The point about many worlds is that most of the states do not exist in our world. Hence the many worlds label.

These states always exist, regardless of event in our world. So there is no collapse to a particular state.

Superposition (as in Engineering) requires all the states to exist together, as they do in my example of molecular bonding.

I never interpreted the many-worlds interpretation that (in my opinion pretty silly) way. What do you call the interpretation where all states do exist in our world?

 

8 hours ago, studiot said:

Have you heard of the LCAO method in Chemistry? (Linear combination of atomic orbitals) It is the simplest attempt to derive bonding from the states of individual atoms by superposition.

Yes. I see no conflict with my interpretation of the many-worlds interpretation.

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1 hour ago, Bender said:

Tomato tomato. How about "Everything stays in superimposed states".

 

I never interpreted the many-worlds interpretation that (in my opinion pretty silly) way. What do you call the interpretation where all states do exist in our world?

 

Yes. I see no conflict with my interpretation of the many-worlds interpretation.

Then you are denying what actually happens in the experiment.

 

According to many worlds, there is a world where there is a decayed nucleus and a dead cat.

In this universe there is no live cat or undecayed version of that particular nucleus.

There is also a different universe with a live cat,  an undecayed nucleus but no dead cat.

 

This principle goes right back to Bohr who originated the idea, and followed through Everett and  Wheeler and then DeWitt.

 

Edited by studiot

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1 hour ago, studiot said:

Then you are denying what actually happens in the experiment.

I don't see how you reached that conclusion.

I guess it depends what you call a "different universe". If your states join the superposition of the cats states (myriads of them, before someone starts nitpicking about two states again), you would be functionally in a different universe, because the different states of you would be entangled with the different states of the cat. In other words: for each state of you, there is only one state of the cat.

There is no reason to assume these different states of you are actually in different universes, even if for all intents and purposes, they might as well be.

It would be silly for an interpretation to not include something basic as LCAO, because then it would not be an interpretation but a hypothesis that is disproven by experiments.

Edited by Bender

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As long as the math works out, does it really matter which interpretation you use ?

An 'interpretation' is sinply us trying to use 'common' sense to describe quantum events.
While the interpretation may spply in some circumstances, it fails miserably in others.
And I believe others have already alluded to this in the preceding page.

My interpretation is that while superposition works at the quantum level, it is silly to consider a cat having differing, superimposed quantum states ( especially alive or dead ). Mostly because a cat doesn't exhibit quantum behavior, so why would you need a quantum mechanical interpretation to describe its behavior ?

( although I could swear my cats can 'tunnel' through walls )

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There are few known algebraic solutions to Schroedinger's equation.

 

One of these is for a single particle translating freely in space.

I don't know who first derived this one or if it was available to Schroedinger, so would appreciate in information abouy that part.

 

Anyway we don't usually use this solution since it contains an enormous number of states, even for a single particle, and 0.5 mv2 is much easier to use.

 

However think about the cat and its particles.

 

All the particles are travelling in the same direction with the same velocity and appropriate KE.

Is this superposition?

Or is it a form of coherence?

Now put the cat into a first class berth on a rocket to Alpha Centauri.

The cat is now in a box, with the same velocity and KE.

Now put the cat in Shroedinger's box within the spaceship.

What, if anything, has changed?

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17 hours ago, MigL said:

As long as the math works out, does it really matter which interpretation you use ?

To make calculations, it doesn't, except perhaps to figure out the best approach to the problem at hand (in which case manyworlds is of little help since all the excessive states are discarded anyway).

It only matters on a philosophical level when trying to figure out QM and trying to fit it into a world view.

Edited by Bender

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On 4/16/2018 at 9:42 PM, Bender said:

Why not? Obviously the cat (and everything around it) can only be in superposition if the isotope can be.

 

Please illuminate me. In my mind, there are billions of atoms interacting, and then the billion-and-first (billion-and-oneth?) particle arrives and spoils the party. Why?

Ok. Is there any evidence that systems ever go to a single eigenstate?

 

Either "none" or "a bunch", depending on whether systems revert to single eigenstates or not.

I have the feeling there is a confusion.

IIRC the cat is linked to the fate of a single particle. Not the entire cat has to be in superposition. The trick of Schrödinger is to directly link a macroscopic phenomenon (the cat live or dead) to a quantum one. By doing so he enhances the "absurdity" of quantum behaviour.

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In the original thought experiment, the cat is simultaneously dead and alive, which is absurd under Copenhagen (which was, and possibly still is, the most prevalent interpretation).

However, when the thought experiment is extended outside its original scope, it leads to the many-worlds interpretation, where the cat is indeed both dead and alive, but in different universes (or states of this universe).

In that case, it is not really absurd, but a great topic to discombobulate people. I have the experience that people (even atheists and materialists) can have a hard time accepting the possibility of different versions of themselves :). The reaction of my students when I touched this subject was always neat.

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On 4/20/2018 at 5:34 AM, studiot said:

There are few known algebraic solutions to Schroedinger's equation.

 

One of these is for a single particle translating freely in space.

I don't know who first derived this one or if it was available to Schroedinger, so would appreciate in information abouy that part.

You have reversed both cause-and-effect and history. Schrödinger derived his equation, for a free particle, from the a priori known Fourier Transform of the wave-packet that he (following de Broglie) "associated" with a particle, as a sort of tracking mechanism. The derivation of the Schrödinger equation for a free particle, consists of little more than computing the first partial derivative of the Fourier transform with respect to time, then the second partial derivative with respect to position, and then equating the two.

image.png.a94fd4dc4d8f2e211181fcd9f7af2efa.png

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3 hours ago, Rob McEachern said:

You have reversed both cause-and-effect and history. Schrödinger derived his equation, for a free particle, from the a priori known Fourier Transform of the wave-packet that he (following de Broglie) "associated" with a particle, as a sort of tracking mechanism. The derivation of the Schrödinger equation for a free particle, consists of little more than computing the first partial derivative of the Fourier transform with respect to time, then the second partial derivative with respect to position, and then equating the two.

Well I see that you have exhibited a Schroedinger equation, but I don't see you exhibiting a solution in explicit form


[math]\Psi \left( {x,t} \right) = ???[/math]


That would be what I call a solution.

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4 hours ago, studiot said:

Well I see that you have exhibited a Schroedinger equation, but I don't see you exhibiting a solution in explicit form

Equation (2) is the general solution!

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15 hours ago, Rob McEachern said:

Equation (2) is the general solution!

 

I'm not entirely sure why you posted a derivation of Schroedinger, or where you are going with it?

Your Schroedinger equation is only true because the potential term is zero, otherwise it is incomplete.

 

The solution I was thinking about is

 


[math]\Psi  = A\sin \sqrt {\left( {\frac{{8{\pi ^2}m}}{{{h^2}}}} \right)} x[/math]

 

Which I think is more useful as you can plug numbers into it.

 

As I understand it, the method of finding this solution is 'inspired guess', which means guessing solutions, based on experience, and testing to see if they satisfy the DE or PDE, which they do in this case.

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6 hours ago, studiot said:

Your Schroedinger equation is only true because the potential term is zero

You stated you were only concerned with solutions "for a single particle translating freely in space": a potential, that has any effect whatsoever on a particle, implies that the particle is not free.

7 hours ago, studiot said:

The solution I was thinking about is

is not even a function of time, so it does not represent anything "translating" anywhere.

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8 hours ago, Rob McEachern said:

You stated you were only concerned with solutions "for a single particle translating freely in space": a potential, that has any effect whatsoever on a particle, implies that the particle is not free.

What about a constant positive potential everywhere?  Would that have an impact on the particle being free?

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