# Schrodinger's Cat solutions

1. Aug 16, 2004

### SeManTics

Yeah, I just wanted to check with you guys-
Have ANY of you come up with your own solutions to Schrodinger's cat?

-Sam

2. Aug 16, 2004

### ZapperZ

Staff Emeritus
Solutions? I didn't know there was a problem!

Zz. [Dreading the thought of having to describe all over again the H2 molecule, the SQUIDS experiments, and Tony Leggett's paper]

3. Aug 16, 2004

### Gonzolo

Shrodinger's cat is not a problem. It is an illustration used to explain an important issue in quantum mechanics.

Simply put, the issue is that the state of a particle or a system of particles is only defined once it is experimentally observed. Before observation, all states can be said to co-exist, and all that can be calculated by QM is the probability of observing each state.

4. Aug 16, 2004

### SeManTics

The idea is, in particular, that there is a cat in a box. In that box is toxic material, and some stuff that could set off that material. Thing is, the box is closed, so we don't know if the toxic stuff was unleashed and killed the cat, or if the cat is still toxin-free and alive. And, as Gonzy put it, the cat exists in two states until we peek inside the box. For years, people have been trying to find an exception to prove the cat exists in only one of those two states, but so far all have failed. :grumpy: :uhh:

5. Aug 16, 2004

### marlon

Once we perform a measurement on the cat (we open the box and look at it), the superposition of the cat's wavefunction is broken. This means that decoherence has taken place and entanglement between the cat and our possible measurement outcomes has occured : we see the cat as either living or that once the box is openend. Prior to that we don't know sqaud besides that the cat-wavefunction is a superposition of living and dead each with chance a half, in order to have a normalized wavefunction...

regards
marlon

6. Aug 16, 2004

### ZapperZ

Staff Emeritus
So what exactly is the problem here? The classical cat (the one that we know and love) is either dead or alive. It is the QUANTUM CAT that puzzled people. We know that at the quantum level, we see every indication that such superposition exists, which is why I mentioned examples from H2 molecules, the SQUID experiments, etc. What is puzzling is, at what SCALE do we lose these effects and get back our classical cat.

However, the Schrodinger Cat itself is not a problem. Superposition of states DO exist!

Zz.

7. Aug 16, 2004

### ZapperZ

Staff Emeritus
I'm going to be a bit picky here and point out that if you make a measurement, while you collapse the wavefunction for that particular measurement, the non-commuting observables are STILL in a superposition of states. It is how we can detect the effects of superpostion of states in, let's say, the H2 molecule. Before a measurement, an electron in an H2 molecule occupies a position around BOTH H atoms simultaneously. If we try to measure the position of an electron being shared by the the two H atoms, we will automatically find the electron localized at either one. So we lose the position superposition this way. But we don't have to measure position to detect this superposition. We can measure the ENERGY state of the H2 molecule. This is because if the electron TRULY are in a superposition where it is simultaneously being shared by both H atoms, then an interesting effect happens - the presence of bonding and antibonding states. These states do not occur if the electron is at either one or the other. It will only occur if there is a superposition of the electron over BOTH atoms simultaneously.

Since the energy operator does not commute with the position operator, a measurement of the energy state will not collapse the position eigenfunctions, so the superposition of the electron over both H atoms in the molecule is preserved.

Moral of the story: the superposition is destroyed only for that operator and all commuting operators (for non-degenerate states).

Zz.

8. Aug 16, 2004

### Gonzolo

Shoot a x-ray through the box, listen for a heart-beat, shake the thing and listen for the associated "EEEAAOOORRWWW" etc. etc. etc. (sorry, couldn't resist)

1. The issue is not about a cat in a box. The cat in the box represents a physical system instruments cannot measure.

2. People who do and use QM don't see a problem. It is people who can't let go of classical determinism who do. Very few of them around these days, besides those who have not seen why QM was needed.

9. Aug 17, 2004

### reilly

First of all, the issue of the well being of Schrodinger's cat has nothing to do with quantum phenomena; it's simply an issue of probability. One can use any number of different classically based processes to trigger the deadly gas. For example, build a machine to flip a coin, and use a neural network or other detector to note heads or tails, and track the total heads. If the number of heads equals some N, then bye-bye cat.

So, what's the problem with noting that the state of the cat is either alive or dead, but not both. We're talking normal reality, not paranormal communication with the dead or quasi-dead, cats or people, or whatever. However, the state of our knowledge of the cat is indeed uncertain; our brain allows as how the cat could be dead, could be alive, who knows - that's the sort of thing brains do. When we find out the truth, then our uncertain neural pattern collapse to the pattern corresponding to alive/dead. It's our knowledge that changes.

This knowledge based approach, that |PSI|*|PSI| represents a normal probability density which reflects the state of our knowledge. That is, the wave function does not have a direct physical reality. Any wave function collapse is then associated with the change in our knowledge. This approach, by the way, is totally consistent with the one successfully used for probability and statistics for the past few centuries.

Least I be accused of being simple-minded, let me assure you that such an eminant Nobelist as Sir. Ronald Peirels is an advocate of this position.

Regards,
Reilly Atkinson

10. Aug 17, 2004

### vanesch

Staff Emeritus
This doesn't work, that is exactly the content of Bell's theorem. But the "cat" experiment doesn't illustrate it.
In fact, now we know that the cat doesn't really exist in a superposition of dead and alive states, because the cat is a macroscopic system that cannot avoid coupling to the environment (thermally, gravitationally...) in such a way that the pure superposition-state quickly evolves to a local statistiscal mixture (that's what decoherence tells us).
I find it funny that people deny the problem, while it is still _the_ outstanding problem in QM (I'm not talking about the cat per se, but about the measurement problem).

cheers,
Patrick.

11. Aug 17, 2004

### ahrkron

Staff Emeritus
In response to Reilly,

The superposition of quantum states is NOT analogous to a simple state of not-knowing. The fact that the system is in a state of superposition can (and does in many cases) have a measurable effect on the experimental outcome; it is the cause of interference in double-slits and of mixing of B hadrons.

12. Aug 17, 2004

### whydoyouwanttoknow

The phone rang. It's the cat. It said for you guys to get in the box and see what you think now.

13. Aug 17, 2004

### ZapperZ

Staff Emeritus
Again, if this is true, then (i) there isn't any paradox/problem/etc and what's the brouhaha about and (ii) H2 molecule would not have the energy gap between the bonding and antibonding state.

The issue here isn't about "probability". The issue here is superpostion of properties where classically, those properties can only acquire EITHER one or the other (or however many possible values). QM wavefunction is saying no, this isn't not the case, and a superposition is a state where ALL the possible outcome are present and intermingling until they are measured.

The SQUID experiments conducted recently at Stony Brook[1] and at Delft[2] CLEARLY showed a case where the supercurrent was flying in BOTH DIRECTIONS simultaneously. It is the ONLY means to attain the two separate states. If the supercurrent is flowing either in one direction OR the other, the effect will NOT be detected.

The same can be said about a 2-slit experiment. It is a superposition of the path through BOTH slits simultaneously. This is the only means to get the interference pattern, implicating that a single photon is interfering with itself. A photon that goes through EITHER one slit or the other will NOT produce the identical interference pattern.

I have mentioned this reference before, but I highly recommend a topical review on this issue by Tony Leggett.[3] There is a huge, substantial but subtle issue that is involved here when discussing the Schrodinger Cat-type states. One cannot fully understand and appreciate QM without knowing and understanding the issues surrounding quantum superposition. When Feynman stated that when you understand the double-slit, you'll understand QM, this is exactly the principle he was refering to!

Zz.

[1] J.R. Friedman et al., Nature v.406, p.43 (2000).
[2] C.H. van der Wal et al., Science v.290, p.773 (2000).
[3] A.J. Leggett J. Phys: Cond. Matt. v.14, p.415 (2002).

14. Aug 17, 2004

### SeManTics

I think the fact that a cat is present in Schrodinger's Wavefunction problem IS significant. See, I'm up here in Canada, and my cousins have two cats. One of these cats meows CONSTANTLY. This tells me, apart from the fact that the cat has an annoying personality, that the cat - like a baby - WANTS. That it the slightest hint of consciousness. I think what Schrodinger's trying to say is: 'What if a being or lifeform with CONSCIOUSNESS is in that box. Would it make a difference if that was the case instead of, say, a twig?' Because the conscious lifeform would KNOW if it was alive.

15. Aug 17, 2004

Staff Emeritus
Schroedinger was a cat lover, and used a cat in his gedanken experiment to give it emotional force. It worked; we discuss the cat and not the SQUIDs that have really shown the effect.

16. Aug 17, 2004

### ZapperZ

Staff Emeritus
I am afraid that you are mising the point of the thought experiment. If let's say we put YOU in the box with the cat, you would know the exact state of the cat, but for the rest of us, the radioactive source + cat + you + box are STILL in a superposition of dead+alive states!

The cat is IRRELEVANT. It is merely an embelishment to the principle. We could eliminated you and the cat and talk about the radioactive source. But as Self-Adjoint has pointed out, the public are more fascinated by something when it has something it can relate to - y'know, fluff over substance. [Hey, Humanino already indicated that I'm in a bad mood this morning. :) ]

The issue that is in the center stage in the Schrodinger Cat experiemnt isn't the cat, it is the superposition principle of QM. Superpostion is REAL at the quantum scale. There are a zoo of phenomena that cannot be explained without such principle. Yet, at the classical scale, this phenomena goes away. It is THIS transition between classical and quantum scale that is the subject of intense study, NOT the validity of classical non-superpostion or quantum superposition principle.

Zz.