# Schroedinger's cat: half-alive and half-dead

#### eehiram

If only "sensible" results of measurements can be observed, how do atomic scientists verify wavefunction states of a phenomenon like a half-live and half-dead Schroedinger's cat? I remember reading that the analogy applies to semiconductor circuits, where a gas exists on both sides of a barrier until it is observed. How can this be known with certainty?

o| Hiram

Related Quantum Physics News on Phys.org

#### ZapperZ

Staff Emeritus
2018 Award
Do a search on here for either "superposition" or "Delft/Stony Brook SQUID" experiment.

Zz.

#### marlon

Another proof of superposition is the very simple and ordinary diatomic hydrogen molecule

marlon

#### eehiram

Thanks for the replies

I'm not sure I understood the article on covalent bonding of the hydrogen molecule, but I know I covered it in high school and college chemistry, so I won't bore you with questions about it here and now.

o| Hiram

#### Martin Brock

Demystifying Quantum Mechanics

Rather than discuss Schrödinger's cat, I'll link Wikipedia.

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

Note that Schrödinger devised this thought experiment to ridicule the idea that a quantum mechanical system assumes a definite state only when it is observed.

What does the term "quantum indeterminacy" mean? Does a quantum mechanical system exist in an indeterminate or mixed state until observed? Does quantum indeterminacy imply that a cat can be neither dead nor alive or half alive and half dead?

I address these questions using only classical physics, so the discussion is more accessible and less mysterious. I describe a simple, "quantum mechanical" device that you could construct yourself. The device is "quantum mechanical", because 1) it absorbs or radiates a quantum of energy when excited, 2) it has discrete, stable states and 3) its state is described in terms of probabilities; however, the device is macroscopic, and I describe it here in classical terms.

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Imagine the rigid body illustrated above. You're looking down on it. The long line (O--O) is a rigid rod fixed at both ends. The shorter lines (M--O) are rigid rods attached to the long rod but free to rotate with the long rod around its axis. The M's are weights free to slide along the short rods. The weight of the rods is insignificant compared with the sliding weights.

Since the system is symmetric about the long rod, it can in principle balance as illustrated under gravity; however, this state of the system is unstable. The system has two stable states.

If the weight on the left drops slightly and the weight on the right rises, the weight on the right slides down its rod, and the whole system quickly arrives at a stable state with the short rod on the left down and the short rod on the right up.

If the weight on the right drops slightly, the system quickly assumes the other stable state with the short rod on the right down and the short rod on the left up.

In either case, before settling into a stable state, the system enters an oscillating state in which the dropping weight swings like a pendulum until friction stops the oscillation. In the process, energy is lost to friction, radiated as heat. Either stable state has less potential energy than the unstable state illustrated.

We can add energy to the system (excite it) by causing it to spin rapidly about the axis of the long rod. Centripetal forces then hold each weight at the outer end of its rod. As friction slows the spinning, the system radiates energy and eventually comes to rest in one of its stable states, but we can't easily predict which one. The final state is thus indeterminate. We can assign equal probability to each state, but these probabilities are all we can know about the system's final state until we observe it.

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If one rod is slightly longer than the other, the system still has two stable states, but the potential energies of the two states are not the same, and the probabilities presumably are not equal. The difference between the two energies is a quantum of energy separating the states. If the system in the lower energy state (long arm down) is excited and returns to the higher energy state, it absorbs a quantum of energy. If the system in the higher energy state (short arm down) is excited and returns to the lower energy state, it releases a quantum of energy.

This system is a classical example of quantized energy. It radiates energy when transitioning from a higher energy state to a lower energy state, as a hydrogen atom radiates energy when an electron "falls" into a "lower" orbital.

Here's the point. After exciting the system, we can't know the next stable state until we observe it, but our observation does not cause the system to collapse into a quantum mechanical state. A loss of energy causes this collapse. Observation does not determine the state (cause the system to assume a state). Observation allows an observer to determine the state. Only observation allows this determination, because only the probabilities of states are known otherwise.

Finally, back to the cat. The quantum of energy emitted during radioactive decay is like the quantum of energy emitted if the system above is excited in the higher energy state and returns to the lower energy state. Observation of the system does not cause this transition. It happens when it happens, and the cat dies when it happens. We can't know precisely when it happens without observation. That's all.

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#### ZapperZ

Staff Emeritus
2018 Award
I don't think this is correct. For some reason, you had to invoke an "excited state" transition, which isn't necessary. You are describing a system in which the final outcome is not known. This is no different than throwing a dice and not knowing which number will turn up.

The Schrodinger cat state illustrates the principle of superposition, and in fact, such superposition CAN be detected if you measure the non-commuting observable. This is what is done in the Delft/Stony Brook SQUID experiment. The coherent energy gap is a direct outcome of such superposition.

Zz.

#### Martin Brock

I don't think this is correct. For some reason, you had to invoke an "excited state" transition, which isn't necessary. You are describing a system in which the final outcome is not known. This is no different than throwing a dice and not knowing which number will turn up.
Explain more specfically what is incorrect. I don't call the state "unknowable". I say, "we can't easily know" it. I'm not suggesting that the device is fundamentally non-deterministic. I say the system is "described" in terms of probabilities. It is like throwing a dice or spinning a roulette wheel. If we don't precisely control and cannot precisely measure the rate of spin during an "excited state", we can't predict the final state.

The Schrodinger cat state illustrates the principle of superposition, and in fact, such superposition CAN be detected if you measure the non-commuting observable. This is what is done in the Delft/Stony Brook SQUID experiment. The coherent energy gap is a direct outcome of such superposition.
Zz.
"Superposition" describes the wave function. The wave function is theoretical. The wave function is a description, not the reality described. I'm not suggesting that superposition and entanglement have no measurable effects in Quantum Mechanics. A coupling of states does involve energy. The states of the left and right rods above are coupled. We could complicate the system by making the long rod less rigid, allowing oscillation of the short rods about the axis of the long rod. The "entanglement" of the two short rods then changes and the coupling between them can store energy.

I am claiming that observation does not cause the wave function to collapse. This point motivates the example. I don't claim to explain the Quantum Mechanical description of a hydrogen atom.

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#### ZapperZ

Staff Emeritus
2018 Award
Explain more specfically what is incorrect. I don't call the state "unknowable". I say, "we can't easily know" it. I'm not suggesting that the device is fundamentally non-deterministic. I say the system is "described" in terms of probabilities. It is like throwing a dice or spinning a roulette wheel. If we don't precisely control and cannot precisely measure the rate of spin during an "excited state", we can't predict the final state.
But that is precisely what is not correct. This has nothing to do with a quantum system.

Before I flup a coin, I know that the outcome of the situation is either heads, OR tail. That is crucial. There was never at any stage where the "reality" of a mixture of heads and tail enters into my physical understanding of the system. In fact, there's nothing that I can measure to indicate that there is a superposition of these two orthorgonal outcome. Even after I flip the coin but don't look at it, the system is in one particular state OR the other, not a superposition of both.

If this is all there is about a QM system, then it wouldn't have been so weird. I am certain that even before QM, people were already gambling and flipping coins. So why would QM be so strange?

This is becuase the superposition of those states (the linear combination of "heads" and "tails") CAN and DO cause a physical property of a QM system. While the act of measurement of an observable causes the system to only reveal ONE possible outcome of that observable, the measurement of an observable that DO NOT COMMUTE with the first observable will produce an outcome that can only be explained if the first observable is in a superposition of states. In other words, before one "collapses" that observable, there ARE detectable measurement that indicates the presence of such superposition where ALL of the possible outcomes are "intermingling" with each other.

I have writen and made citations to relevant papers on this many times (one can do a search on here). I will simply quote what I've written elsewhere if you wish to check on this yourself:

ZapperZ said:
These are the papers that clearly show the Schrodinger Cat-type states (alive+dead, and not alive or dead). All the relevant details are there and anyone interested should read them. Also included is the reference to a couple of review articles which are easier to read, and the reference to two Leggett's papers, who was responsible in suggesting this type of experiments using SQUIDs in the first place. Again, the papers have a wealth of citations and references.

The two experiments from Delft and Stony Brook using SQUIDs are:

C.H. van der Wal et al., Science v.290, p.773 (2000).
J.R. Friedman et al., Nature v.406, p.43 (2000).

Don't miss out the two review articles on these:

G. Blatter, Nature v.406, p.25 (2000).
J. Clarke, Science v.299, p.1850 (2003).

However, what I think is more relevant is the paper by Leggett (who, by the way, started it all by proposing the SQUIDs experiment in the first place):

A.J. Leggett "Testing the limits of quantum mechanics: motivation, state of play, prospects", J. Phys. Condens. Matt., v.14, p.415 (2002).

A.J. Leggett "The Quantum Measurement Problem", Science v.307, p.871 (2005).

This paper clearly outlines the so-called "measurement problem" with regards to the Schrodinger Cat-type measurements.
"Superposition" describes the wave function. The wave function is theoretical. The wave function is a description, not the reality described. I'm not suggesting that superposition and entanglement have no measurable effects in Quantum Mechanics. A coupling of states does involve energy. The states of the left and right rods above are coupled. We could complicate the system by making the long rod less rigid, allowing oscillation of the short rods about the axis of the long rod. The "entanglement" of the two short rods then changes and the coupling between them can store energy.

I am claiming that observation does not cause the wave function to collapse. This point motivates the example. I don't claim to explain the Quantum Mechanical description of a hydrogen atom.
You have attempted to highlight a lot of issues that aren't related to the original Schrodinger Cat experiment, including "entanglement", which isn't part of the SC-type scenario. The main principle that is relevant here is the principle of superposition. Considering that you did verify my description of your system as identical to flipping a dice or a coin, this then confirms to me that it is not an illustration of superposition. Schrodinger could have easily illustrated this thought experiment by flipping a coin if this were the case. Yet, he chose something else to illustrates the "weirdness" of QM.

Zz.

#### Martin Brock

But that is precisely what is not correct. This has nothing to do with a quantum system.
As I said, I describe a classical system. The system is "quantum mechanical" in the sense I describe above, i.e. it can absorb and release a quantum, and it has discrete states described in terms of probabilities. I nowhere claim to describe a Quantum Mechanical system in terms of modern physics.

Before I flup a coin, I know that the outcome of the situation is either heads, OR tail. That is crucial. There was never at any stage where the "reality" of a mixture of heads and tail enters into my physical understanding of the system.
There is no literal "mixture" of dead and living cats either. That's my point. We can call the spinning system a "mixture" of "left up-right down" and "left down-right up" states if we want, but we mustn't take this description too literally, and the description has nothing to do with any cause of a transition to a stable state.

In fact, there's nothing that I can measure to indicate that there is a superposition of these two orthorgonal outcome. Even after I flip the coin but don't look at it, the system is in one particular state OR the other, not a superposition of both.
I believe the measurable effect in SQUID is entanglement, not superposition.

If this is all there is about a QM system, then it wouldn't have been so weird. I am certain that even before QM, people were already gambling and flipping coins. So why would QM be so strange?
"Weird" and "strange" are not pedagogically useful descriptions. People were flipping coins before QM, and Einstein doesn't like a God throwing dice, but I have no problem with Her.

This is becuase the superposition of those states (the linear combination of "heads" and "tails") CAN and DO cause a physical property of a QM system.
Again, I think you're discussing entanglement here; however, if you want to correct me, that's fine.

While the act of measurement of an observable causes the system to only reveal ONE possible outcome of that observable, the measurement of an observable that DO NOT COMMUTE with the first observable will produce an outcome that can only be explained if the first observable is in a superposition of states. In other words, before one "collapses" that observable, there ARE detectable measurement that indicates the presence of such superposition where ALL of the possible outcomes are "intermingling" with each other.
The first observable is in a state we can call "indeterminate" or "indefinite" or possibly "unstable", as when the short rods are horizontal rather than vertical. The nature of the system then does not tell us where the weights are along the rods.

Imagine two more short rods with sliding weights pointing in opposite directions at right angles to the rods illustrated above. The illustrated rods are x, and the new rods are z. If the z rods are vertical when the system is still, you know the positions of weights on these rods, but what do you know about weights on the x rods in this configuration? In this scenario, the state of the x rods are indeterminate when the state of the z rods are determined and vice versa.

Again, I'm offering classical analogies here to aid understanding. I'm not describing the particular Quantum Mechanical systems you mention. If you want to describe them in greater detail, that's fine.

I have writen and made citations to relevant papers on this many times (one can do a search on here). I will simply quote what I've written elsewhere if you wish to check on this yourself:
I believe you, and I'm not disputing your expertise here.

You have attempted to highlight a lot of issues that aren't related to the original Schrodinger Cat experiment, including "entanglement", which isn't part of the SC-type scenario.
Schrodinger's Cat is not an experiment. I didn't raise "entanglement" here until you raised SQUID. I'm trying to make a point about causation for the benefit of someone without extensive exposure to modern physics.

The main principle that is relevant here is the principle of superposition. Considering that you did verify my description of your system as identical to flipping a dice or a coin, this then confirms to me that it is not an illustration of superposition. Schrodinger could have easily illustrated this thought experiment by flipping a coin if this were the case. Yet, he chose something else to illustrates the "weirdness" of QM.
Zz.
If you want to discuss SQUID, an energy coherence gap and these other subjects, that's fine. My point is different.

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#### ZapperZ

Staff Emeritus
2018 Award
As I said, I describe a classical system. The system is "quantum mechanical" in the sense I describe above, i.e. it can absorb and release a quantum, and it has discrete states described in terms of probabilities. I nowhere claim to describe a Quantum Mechanical system in terms of modern physics.
But the Schrodinger cat-state involves NO "transition" between energy levels, nor "absorbe and release" of a "quantum" of anything. That is what I've been trying to get across. Your example have nothing to do with the topic of this thread, which is the superposition of orthorgonal states as illustrated in the Schrodinger Cat scenario.

There is no literal "mixture" of dead and living cats either. That's my point. We can call the spinning system a "mixture" of "left up-right down" and "left down-right up" states if we want, but we mustn't take this description too literally, and the description has nothing to do with any cause of a transition to a stable state.
Again, there is no transition of any kind, or of a 'stable' state. ALL the states in the superposition ARE "stable".

I believe the measurable effect in SQUID is entanglement, not superposition.
You are wrong. I suggest you read those papers, especially Tony Leggett's extensive paper on the measurement problem and the conclusion of both experiments.

Please note that this thread is a discussion of a specific issue regarding superposition. If your system, by your admission, doesn't illustrate a quantum superposition, then you have brought up an example that is not relevant to the thread, and in fact, may add confusion to it. You have already stated that your example is identical to the classical probability. It makes no sense to equate this to a quantum system, and it shouldn't. Thus, it has no relevance to this topic.

Zz.

#### Martin Brock

The Schrodinger's Cat thought experiment does involve release of a quantum. Radioactive decay releases a photon triggering a geiger counter to release a poison killing the cat.

I'm off to work and can't play further now, but I'll return later. If I'm wrong about entanglement in the SQUID experiment, thanks for the correction. I can't agree with your limitation of the topic, but you may discuss your grievance with the moderator.

#### ZapperZ

Staff Emeritus
2018 Award
The Schrodinger's Cat thought experiment does involve release of a quantum. Radioactive decay releases a photon triggering a geiger counter to release a poison killing the cat.
You are confusing the source with the principle of the scenario. This is where if you ONLY understand the description without understanding the mathematics (which is what Schrodinger was trying to illustrate in the first place), then you only saw the shadow of the animal without fully seeing the animal itself.

The emission of the "radioactive particle" is actually incidental to the scenario. All that was supposed to do is add the quantum probability into the system. That's it. If flipping a coin is a quantum process, then schrodinger would have used it to trigger the poison. He didn't because it isn't a quantum process that's governed by quantum probability as interpreted by the Copenhagen school.

Note that when a photon passes through a 2-slit experiment, that IS also an example of superposition. In fact, there are MANY processes that are clear illustration of superpostion (bonding-antibonding bands in H2 molecule). None of these produces an "energy release". You are stuck with an example while ignoring the principle that is being illustrated. By doing that, you have somehow illustrated exactly what I described in one of my essays on why QM is so difficult to understand when people do not have a solid grasp of its mathematical formalism.

I'm off to work and can't play further now, but I'll return later. If I'm wrong about entanglement in the SQUID experiment, thanks for the correction. I can't agree with your limitation of the topic, but you may discuss your grievance with the moderator.
I AM one of the moderator!

Zz.

#### Tomsk

Can we take the view that Schrodinger's Cat is an observer too, and could break out of his box to find a 28 Days Later/Day of the Triffids type situation (which would have to be in a superposition with a bunch of scientists sitting around waiting for the results, as well as any other possible scenario, before he broke out)? If not why not?

#### ZapperZ

Staff Emeritus
2018 Award
Can we take the view that Schrodinger's Cat is an observer too, and could break out of his box to find a 28 Days Later/Day of the Triffids type situation (which would have to be in a superposition with a bunch of scientists sitting around waiting for the results, as well as any other possible scenario, before he broke out)? If not why not?
This is now veering into metaphysics, which, if you've been around long enough, you'll know how much I detest. There is a rather nasty corner of CI which claims that each time an observation is made, the system plus the observe is now in a superposition of state, and so on and so on ad nauseum.

I don't buy that, mainly because there's no experimental observation that illustrates that. It is also irrelevant from the point of view that if QM "weirdness" can be chain-linked like that, we would have seen the effects at the macroscopic level and it won't be so unusual. We need to keep in mind that decoherence is extremely easy to set in, and very difficult to keep out. The Delft/Stony Book experiments aren't significant because it illustrates superposition at work (we have tons of examples of superposition from chemistry), but rather they showed it at work for 10^10 electrons, which is considered HUGE by all standards. This wasn't easy to do.

Zz.

#### eehiram

Perhaps I can be of some assistance in quenching this debate...

...since I started the thread originally and I can explain what I was looking for:

First, Martin Brock, thank you for your attempt to assist me with, as you said, a classical physics example. Let us say that it is worth what all classical physics examples are worth in trying to explain QM, and now proceed to return to QM, as I have about a high school level understanding of it.

And ZapperZ, thanks for your attempts to elucidate me, although some of your technical terms are a bit unclear to me. I will hopefully try to learn about the SQUID experiment, but I have not done so yet.

Having addressed both of you, let me get to my original point:

What I meant by asking about the superposition of a half-living and half-dead cat is simply that, unlike the living and dead states, the half-and-half state can not be observed once the box is opened. Only "sensible" states can be observed. How then is the half-and-half state verified? Is there some experiment by which it can be detected, and thus it's equation is therefore validated? Perhaps the SQUID experiment is that experiment. But without mincing words ("detected" vs. "observed"), as I already recognized the half-and-half is not "sensible" and can not be observed -- not directly -- in any experiment that involved anything like observation. It always collapses to either a living or a dead state upon observation.

I hope this clears things up. However, I love anything QM-related and enjoyed reading your debates on the differences between classical coin flipping and QM superposition and wavefunction collapsing, as that is something I go through in trying to explain QM to my therapist Paul. To my credit, I have done a lot of self-taught education (skipping the mathematical equations) on QM, and my therapist Paul has not.

This is only my second thread, and I just wanted to get the ball rolling. I would also like to discuss the Copenhagen school and its objectors in a third thread, as that seems to be coming up here in this forum.

o| Hiram

#### ZapperZ

Staff Emeritus
2018 Award
...since I started the thread originally and I can explain what I was looking for:

First, Martin Brock, thank you for your attempt to assist me with, as you said, a classical physics example. Let us say that it is worth what all classical physics examples are worth in trying to explain QM, and now proceed to return to QM, as I have about a high school level understanding of it.

And ZapperZ, thanks for your attempts to elucidate me, although some of your technical terms are a bit unclear to me. I will hopefully try to learn about the SQUID experiment, but I have not done so yet.

Having addressed both of you, let me get to my original point:

What I meant by asking about the superposition of a half-living and half-dead cat is simply that, unlike the living and dead states, the half-and-half state can not be observed once the box is opened. Only "sensible" states can be observed. How then is the half-and-half state verified? Is there some experiment by which it can be detected, and thus it's equation is therefore validated? Perhaps the SQUID experiment is that experiment. But without mincing words ("detected" vs. "observed"), as I already recognized the half-and-half is not "sensible" and can not be observed -- not directly -- in any experiment that involved anything like observation. It always collapses to either a living or a dead state upon observation.
But see, that is what I've been trying to illustrate to you when I talk about measuring a "non-commuting" observable. I believe I've mentioned this several times.

The problem with trying to understand QM devoid of the mathematical formalism is that you end up being told, out of thin air, certain things that would make no sense. This is because you cannot use your everyday understanding as the foundation to understand QM. It is THAT disconnected. Therefore, if I tell you that the Schrodinger Cat experiment is really an illustration of this:

$$|\Psi> = a_1|\psi_1> + a_2|\psi_2>$$

you'd groan and walk away. Yet, this is exactly what Schrodinger is trying to show. We must always go back to the source to get the complete and accurate picture. What you measure, which we call an observable, is represented by an operator. The commuting properties of 2 different operators or observable is a CENTRAL formulation of quantum mechanics (some even call it First Quantization). So you see, a lot of the "words" we describe here are really, truly based on our foremost understanding of the mathematics first. We then try to put into words (often in very awkward way) what these mathematics mean, which becomes our interpretation. Unfortunately, such interpretation can be ambiguous, leading to several different interpretations. Yet, the initial source, the formalism, remains the same.

Those $\psi$ can be anything. It could be a dead and alive state, left and right slits, position x1 and x2, etc... and in the Delft/Stony Brook experiment, current moving in direction and another. All of these different experiments and observations ALL illustrates the IDENTICAL PRINCIPLE. It just happens that the general public simply caught on with the Cat (which was the purpose of Schrodinger's illustration) and not, let's say, with a H2 molecule.

If it isn't clear by now, I'll say it again. The effects of superposition is VERY clear, especially in chemistry, where many of what chemists have measured can be described by such a scenario. The issue now isn't if superposition is present, but rather why is it present at the microscopic, quantum scale, but not at our macroscopic, classical scale. That is now the issue, not if it is valid or not.

Zz.

#### eehiram

Alright, ZapperZ

I of course must defer to your mathematical explanation, although I'm not that clear on what it means. I'm familiar with the psi character, but not the rest of it.

It's alright, though. I know I would need to get a B.S. in physics to really understand QM a lot better. Currently, I'm hoping to get an A.A. in physics, perhaps, but I don't plan to return (I dropped out) to 4 year university. So for now, unfortunately as you indicated, the laymen's explanations will be all I can handle.

Thanks for your valiant attempts to elucidate me, though.

o| Hiram

#### Martin Brock

But the Schrodinger cat-state involves NO "transition" between energy levels, nor "absorbe and release" of a "quantum" of anything. That is what I've been trying to get across. Your example have nothing to do with the topic of this thread, which is the superposition of orthorgonal states as illustrated in the Schrodinger Cat scenario.

Again, there is no transition of any kind, or of a 'stable' state. ALL the states in the superposition ARE "stable".
The release of a quantum of energy involves a state transition, and Schrodinger's Cat dies when a quantum is released. I linked an article with Schrodinger's description of the thought experiment. Here it is.

"One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

"It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality."

You are wrong. I suggest you read those papers, especially Tony Leggett's extensive paper on the measurement problem and the conclusion of both experiments.
If the experiments don't involve entanglement, so be it. You're the physicist here.

Please note that this thread is a discussion of a specific issue regarding superposition. If your system, by your admission, doesn't illustrate a quantum superposition, then you have brought up an example that is not relevant to the thread, and in fact, may add confusion to it. You have already stated that your example is identical to the classical probability. It makes no sense to equate this to a quantum system, and it shouldn't. Thus, it has no relevance to this topic.

Zz.
The thread announces itself as a discussion of Schrodinger's Cat, and Schrodinger himself devised the thought experiment to ridicule the idea of a cat in mixture of states in which it is either living or dead. The cat dies when a quantum is emitted. I don't doubt your expertise, but I suppose Schrodinger had some point he wanted to make, and his point seems to be that observation of the cat does not replace a half-emitted quantum and a half-dead cat with a fully emitted quantum and a fully dead cat.

My point remains that observation does not cause a quantum mechanical state transition, like the transition associated with emission of a photon. Observation reveals a state. A system can exist in an intermediate or indeterminate state or a superposition of states.

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#### Martin Brock

You are confusing the source with the principle of the scenario. This is where if you ONLY understand the description without understanding the mathematics (which is what Schrodinger was trying to illustrate in the first place), then you only saw the shadow of the animal without fully seeing the animal itself.
Schrodinger was suggesting that a cat in a mixture of living and dead states is ridiculous.

Since we're announcing credentials here, I'll announce mine. I have a masters in applied mathematics, focusing on probability and stochastic processes, from the University of Alabama in Huntsville with a 4.0 grade point average. I didn't pursue a phd there, because I exhausted course work at this level pursuing the masters, and I didn't want to pursue an intercampus course of study.

My undergraduate degree is in computer science with a double major in physics. I didn't quite finish the physics major, because I wanted to marry and work after four years. Finishing the CS major was easier and created more employment opportunity. I'm thoroughly working class. I did progress through a first course in Quantum Mechanics. I understand the relevant mathematics. What I understand less well than you, no doubt, is the physics, experimental details and the like, and I'm happy to have your instruction; however, your audience here is not familiar with much of the terminology you use. Recommending technical papers is fine, but we don't need this forum to read technical papers.

I worked in an experimental physics lab (astrophysics) for eleven years as a data analyst and have a few publications in the area, but I have never been a professional physicist or worked with particle physics. I worked with gamma ray spectroscopy, but the work involved no applications of Quantum Mechanics. I certainly acknowledge your wider experience in this regard.

The emission of the "radioactive particle" is actually incidental to the scenario. All that was supposed to do is add the quantum probability into the system. That's it. If flipping a coin is a quantum process, then schrodinger would have used it to trigger the poison. He didn't because it isn't a quantum process that's governed by quantum probability as interpreted by the Copenhagen school.
It's not incidental to Schrodinger's point, and I'm trying to address Schrodinger's point.

Note that when a photon passes through a 2-slit experiment, that IS also an example of superposition. In fact, there are MANY processes that are clear illustration of superpostion (bonding-antibonding bands in H2 molecule). None of these produces an "energy release". You are stuck with an example while ignoring the principle that is being illustrated. By doing that, you have somehow illustrated exactly what I described in one of my essays on why QM is so difficult to understand when people do not have a solid grasp of its mathematical formalism.
I'm not denying superposition of states. I'm denying that observation causes a quantum mechanical system to enter a discrete state associated with the release of a quantum, which seems to be Schrodinger's point. I constructed an example with an energy release, because Schrodinger constructed an example with an energy release. I constructed a macroscopic, classical example, because people more easily comprehend this example.

I AM one of the moderator!

Zz.
I'm not here to tread on your turf. I hope you'll tolerate my participation.

#### Martin Brock

...since I started the thread originally and I can explain what I was looking for:

First, Martin Brock, thank you for your attempt to assist me with, as you said, a classical physics example. Let us say that it is worth what all classical physics examples are worth in trying to explain QM, and now proceed to return to QM, as I have about a high school level understanding of it.
You're welcome. Macroscopic, classical systems with properties we observe in Quantum Mechanical systems aid understanding in my opinion. ZapperZ apparently disagrees.

What I meant by asking about the superposition of a half-living and half-dead cat is simply that, unlike the living and dead states, the half-and-half state can not be observed once the box is opened. Only "sensible" states can be observed.
As Schrodinger himself suggests, the half-and-half or indeterminate state does not apply to the cat. It applies to a quantum mechanical system. The system enters a discrete, lower energy state, which is not an indeterminate or mixed state, and this transition is associated with emission of a quantum of energy (a photon), and this photon kills the cat. The undetermined or mixed state does not involve any half emitted photon or half-dead cat. This is my only point. I don't deny that systems exist in indeterminate or mixed states, and I don't claim to tell you how a superposition of states is measured. I suggest, by classical analogy, how to imagine a quantum mechanical system in an indeterminate state.

Good luck with your studies.

#### eehiram

Martin Brock, I'm sorry the two of you are fighting

Macroscopic, classical systems with properties we observe in Quantum Mechanical systems aid understanding in my opinion. ZapperZ apparently disagrees.
In my humble opinion, as someone who has studied QM in high school physics, chemistry, and biology classes, I think classical systems are useful to introduce a classically educated science student to the quantum level. High school students fit that bill, as they have been taught almost nothing but the classical science up until about 9th or 10th grade.

On the other hand, once that transitional explanation occurs, it's time to shift gears to the quantum level completely, as much labor goes into explaining the differences between classical science and quantum science. Over and over again, "The electron is not like a planet orbiting the nucleus as the Sun." "The electron probability cloud is the volume of space around the nucleus where the electron might be found at any time, but it does not exist in one specific point, exactly." and other such explanations.

In the case of the debate in this thread, the probability of flipping coins and not looking at the coin right away is similar to quantum probabilities, but in fact there is no debate as to the coin in fact being head or tail without looking at it. Not so in quantum world, claims the Copenhagen school. Whether or not they are right I'm not sure, but in the other schools of interpretation some other weirdness must come into play to make the quantum coin heads or tails for sure without looking at it.

However, your intentions were to help me understand something and I personally abstain from fully taking either side in this emerging argument the two of you are having here.

My preference, if anyone wants to know, is to try to state things along quantum lines -- wtih a high school physics or chemistry level of understanding, so no differential Schrodinger equations, however helpful they are supposed to be -- rather than go backwards to classical systems, as those lead me astray and then we have the debt of all the explanations of differences to pay down the road.

(My own opinion on K-12 classical science education is that, with computers on every desk in the 21st century, it will become more viable to start teaching quantum science earlier on in K-12, perhaps running parallel with classical science; that way classical assumptions don't have to be so jarringly thrown out the window with the Copenhagen school. Similarly with Einstein's 2 theories. One needs 3-D animation and virtual reality capable computers though.)

As Schrodinger himself suggests, the half-and-half or indeterminate state does not apply to the cat. It applies to a quantum mechanical system. The system enters a discrete, lower energy state, which is not an indeterminate or mixed state, and this transition is associated with emission of a quantum of energy (a photon), and this photon kills the cat.
In regards to the cat and the quantum release that triggers poison gas, it was my understanding that the cat, being in the box, goes into an entanglement with the quantum release and this entanglement decoheres when the box is opened and the cat, living or dead, is observed. However, this is the Copenhagen interpretation again, the one taught first and foremost in my introductory books.

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#### ZapperZ

Staff Emeritus
2018 Award
There are so many misinterpretation on so many levels here, I do not know where to begin.

The release of a quantum of energy involves a state transition, and Schrodinger's Cat dies when a quantum is released. I linked an article with Schrodinger's description of the thought experiment. Here it is.

"One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

"It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality."
There no "energy release" here at all. If it is, then it would NOT be identical to the 2-slit experiment. It is you who would have to content to two experiment that are different, yet quantum mechanically of the same principle. The presence if a radioactive decay is there ONLY to provide the source of the "probability". That's all. If not, Schrodinger would have have a source of the "wavefunction" in his scenario. Again, like I said, he could have easily had a different mechanism.

If the experiments don't involve entanglement, so be it. You're the physicist here.
Don't take my word for it. Prove that it has one. Show me where in the formulation that there is a form that looks like

|psi> = a1|u1, v2> + a2|u2, v1>

This is the formal form of ANY entanglement as described in QM (and those EPR-type experiments). Show me where in the physics of the Schrodinger-cat type measurement, this form is central to it description.

The thread announces itself as a discussion of Schrodinger's Cat, and Schrodinger himself devised the thought experiment to ridicule the idea of a cat in mixture of states in which it is either living or dead.
You got this all wrong. Schrodinger never intended to ridicule the situation. I have said this before, but you obviously missed it. If he illustrates the weird quantum properties with H2 molecule, no one other than physicists would pay attention. He used something that other people would understand (and maybe emphathized). This has nothing to do with ridiculing superposition. It is to illustrate that if you carry over what we know to occur at the quantum scale, the result looks very strange.

The cat dies when a quantum is emitted. I don't doubt your expertise, but I suppose Schrodinger had some point he wanted to make, and his point seems to be that observation of the cat does not replace a half-emitted quantum and a half-dead cat with a fully emitted quantum and a fully dead cat.

My point remains that observation does not cause a quantum mechanical state transition, like the transition associated with emission of a photon. Observation reveals a state. A system can exist in an intermediate or indeterminate state or a superposition of states.
This is very difficult to understand. The observation "collapses" the wavefunction, putting it into one of the EIGENSTATE of the wavefunction. You are clear on this, no? It was you who stated that it causes a transition, even an energy emission [you continue to argue with me about a radioative particle being emitted to support your argument]. I was the one who argued that such a thing is incidental. It is there only to introduce a "source", not in the physical sense, of the wavefunction to act on the system. This is where the probability come from. If I use a photon passing through a slit, then the "source" would be the 2 paths that the photon can take. It is the same thing. The central issue is the superposition of several orthogonal states. That's it!

I'm not denying superposition of states. I'm denying that observation causes a quantum mechanical system to enter a discrete state associated with the release of a quantum, which seems to be Schrodinger's point. I constructed an example with an energy release, because Schrodinger constructed an example with an energy release. I constructed a macroscopic, classical example, because people more easily comprehend this example.
And this confuses me even more. What in the world is the "release of a quantum"? When I open the box to finally make the determination if the cat is dead or alive, what "quantum" was released? If I make the determination which slit the photon passed through, what "quantum" was released? If I make the determination which direction the supercurrent was flowing in the Delft/Stony Brook experiment, what "quantum" was released? If I measure which position the electron was at in an H2 molecule, what "quantum" was released?

And notice, you STILL insist on an energy release here. Yet, you just finised telling me that this isn't a QM transition. This "energy" just appear out of nowhere without any form of transition?

What is even more confusing is that you seem to indicate that a "collapse" of the wavefunction upon an observation doesn't occur. This is strange because this is what is most obvious. You determine, without any ambiguity, the staet of the cat upon observation. I thought this was a done deal? You NEVER observe a photon going through BOTH slits if you try to measure it's position. It will always give you one OR the other. It is ONLY when you make a measurement that does not commute with the original operator would you then preserve such superposition.

This has gotten very confusing, and I seem to be repeating the same thing over and over again, which is getting to be rather tedious. You have not demonstrated anything that allows me to conclude that you have even understood the principle behind the Schrodinger-Cat type experiments beyond a misunderstood, superficial idea. It is why your analogy with a classical demonstration isn't valid. If you disagree with it, then may I suggest that you properly formulate the idea and submit it to, let's say, Am. J. of Phys., which publishes things like this. I can certainly vouch for it being "new" and something I've never come across before, but I certainly cannot support the idea that it is a valid analogy.

Zz.

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#### Martin Brock

There are so many misinterpretation on so many levels here, I do not know where to begin.

...

You got this all wrong. Schrodinger never intended to ridicule the situation. I have said this before, but you obviously missed it. If he illustrates the weird quantum properties with H2 molecule, no one other than physicists would pay attention. He used something that other people would understand (and maybe emphathized). This has nothing to do with ridiculing superposition. It is to illustrate that if you carry over what we know to occur at the quantum scale, the result looks very strange.
"One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, ... It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality."

I'm quoting Schrodinger himself here. These words are Schrodinger's description of the thought experiment. He isn't ridiculing the idea of an indeterminate state in a quantum mechanical system. He is ridiculing the idea that of a half-emitted photon and a half-dead cat. No indeterminate state implies a half-emitted photon or a half-dead cat, and observation of a system does not cause the system to leave an indeterminate state and enter a definite state. Observation reveals a definite state. "Undetermined until observed" does not mean that observation itself causes the end of a mixed or indeterminate state (a state that is not an eigenstate). It means that we can't know a specific state until we've observed it.

This is very difficult to understand. The observation "collapses" the wavefunction, putting it into one of the EIGENSTATE of the wavefunction.
The eigenstates of the system are time-invariant, steady states with a discrete energy. It's not so difficult to understand if we don't take the half-dead cat literally, and Schrodinger doesn't want us to take the half-dead cat literally. Schrodinger specifically denies that an indeterminate or mixed state, in which the photon might or might not have been emitted and killed the cat, exists. This denial is the whole point of his thought experiment. Again, I've quoted Schrodinger himself directly in this regard. He isn't denying superposition. He's denying that a half-dead cat is what "superposition" means in this scenario.

You are clear on this, no?
I understand the eigenstates of a system described by Schrodinger's equation, and I understand the mathematics of characteristic values of certain differential equations more generally. The mathematics existed before Quantum Mechanics. Schrodinger apparently applied an equation that he already knew to have eigenvalues described by the Balmer expression for the energy of the spectral lines of hydrogen. Bohr developed his model similarly. The eigenvalues were known empirically before Schrodinger's equation.

eehiram might be interested to know that Balmer was a math teacher at a girl's school in Switzerland and not a research scientist by profession.

I need to prepare for work this morning. I'll respond further later.

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#### ZapperZ

Staff Emeritus
2018 Award
"One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, ... It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality."

I'm quoting Schrodinger himself here. These words are Schrodinger's description of the thought experiment. He isn't ridiculing the idea of an indeterminate state in a quantum mechanical system. He is ridiculing the idea that of a half-emitted photon and a half-dead cat. No indeterminate state implies a half-emitted photon or a half-dead cat, and observation of a system does not cause the system to leave an indeterminate state and enter a definite state. Observation reveals a definite state. "Undetermined until observed" does not mean that observation itself causes the end of an indeterminate state. It means that we can't know a specific, determinate state until we've observed it.
But it is RIDICULOUS if you try to apply it IN THE CONTEXT of our classical world, where two properties that are different are now intermixing simultaneously! He wasn't ridiculing QM, nor superposition! Talk about taking things out of context! And since when did Schrodinger wrote in English?!

But really, this is besides the point. We ALL know (don't we?) that quantum behavior IS "weird". That's the whole point of all of these demonstrations and thought experiments. Einstein tried to do that with EPR, and Schrodinger tried to show how weird it is using his Cat experiment. I will against tell you right away that if he had used H2 molecule as an example, you won't be so captivated by it and we won't be having this conversation. It is AS "ridiculous" when applied to the H2 molecule where an electron occupies two different locations simultaneously.

All of this is what is meant by the wavefunction having a linear superposition of ORTHORGONAL basis states! This is what is "ridiculous" as far as classical mechanics is concerned.

The eigenstates of the system are time-invariant, steady states with a discrete energy. It's not so difficult to understand if we don't take the half-dead cat literally, and Schrodinger doesn't want us to take the half-dead cat literally. Schrodinger specifically denies that an indeterminate or mixed state, in which the photon might or might not have been emitted and killed the cat, exists. This denial is the whole point of his thought experiment. Again, I've quoted Schrodinger himself directly in this regard. He isn't denying superposition. He's denying that a half-dead cat is what "superposition" means in this scenario.
First of all, what is a "half-dead cat"? If you LOOK at the cat, the cat will either be DEAD, or ALIVE. The "observable" for "deadness" and "aliveness" is NEVER "half-dead". The same thing with the 2-slit. The position observable if you measure it, will detect only a photon passing through the left slit, or the right slit, never "half-right" or "half-left".

So already you are either consciously, or unconsciously causing an immediate confusion. So if you care so much about the exact "words" that Schrodinger used (assuming you TRUST the translation and that you put more emphasis on the "words" rather than the mathematics), then you have already used phrases that have vague meanings.

Let's settle this once and for all.

1. Would you say that this is an example of a quantum wavefunction that one would get by solving a schrodinger equation, where the u's are orthornormal basis functions?

$$|\Psi> = a_1|u_1> + a_2|u_2> + a_3|u_3> + ... a_N|u_N>$$

2. If you do, then do you accept one of the postulates of quantum mechanics that states that such wavefunction, in principle, describes ALL the properties of that system upon a measurement of an observable?

3. If you accept #1 and #2, tell me what happened if you make a single measurement of an observable that is an eigen-operator of the basis function represented by the u's.

4. Assuming you have completed #3, compare what you got with the ORIGINAL description of the system, which is $|\Psi>$. Now tell me, in your own words, not Schrodinger's, the difference between the two.

Zz.

#### MeJennifer

We ALL know (don't we?) that quantum behavior IS "weird".
I do not think that knowledge has anything to do with it. Finding something weird is an attitude not knowledge.

I do not find it weird at all. Clearly we are not smart enough to understand it. So I find it incomprehencible but not weird.

To call something weird because we do not understand it is a cop out IMHO.

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