What makes schrodinger cat quantum?

[Adrian59]

The problem here is that you're making an argument based on a matter of TASTES. I made an argument based on available empirical observations. The FACT that we have no "weird quantum-like phenomena" at the classical scale is my evidence. Despite what has been claimed about coin tossing, we have never, ever detected the effects of superposition of states of [head,tail]. We have, however, detected effects of superposition when 10^11 supercurrent flows simultaneously in two opposite directions.

Experimental evidence trumps any and all theoretical assertions.

Zz.

It appears you are moving towards a consensus despite a mild disagreement about the experimental evidence. I couldn't agree more with the last line of the above quote however one shouldn't lose sight of the fact that this thread is all about a thought experiment so that other thought experimental points should be valid - even the great Steven Weinberg used a head / tails analogy in his Dirac memorial lecture (Cambridge University Press). Also as has been commented, QM is deterministic at the wave function level. It is when we essentially ask binary questions like is the cat dead or alive that QM appears probablistic. I suspect that the cat is classical and though not actually shielded from decoherance as commented by another contributor we are mentally delaying the discovery of its fate so that in effect we're delaying the point where we discover decoherance has taken place.

 

[Count Iblis]

Decoherence is a red herring here, as all it will do is make a superposition that is confined to the box to transform into a global superposition.

I strongly disgree with ZapperZ's denialism by hiding behind what can be directly measured in experiments. It should be clear that you won't be able to detect superpositions involving heads and tails, just like you won't be able to verify that Nature is really time symmetric at the macro level.

I.e. I take a gram of salt and poor that into a litre of water. This process is reversible at the micro-level given all we know about physics. Why then does ZapperZ not dispute this also by demanding a direct experimental verification?

 

[ZapperZ]

Decoherence is a red herring here, as all it will do is make a superposition that is confined to the box to transform into a global superposition.

I strongly disgree with ZapperZ's denialism by hiding behind what can be directly measured in experiments. It should be clear that you won't be able to detect superpositions involving heads and tails, just like you won't be able to verify that Nature is really time symmetric at the macro level.

I.e. I take a gram of salt and poor that into a litre of water. This process is reversible at the micro-level given all we know about physics. Why then does ZapperZ not dispute this also by demanding a direct experimental verification?

But you CAN detect such superposition! That's the whole point of Leggett's paper, the existence of the coherence gap in the Delft/Stony Brook experiments. Did you even READ those papers? It is NOT just MY interpretation of it.

If you disagree, then write a rebuttal to Leggett's paper and to those two experimental paper and tell them that the coherence gap has NOTHING to do with the superposition of the supercurrent flow! Till then, your opinion on here really has zero value.

Zz.

 

[Count Iblis]

But you CAN detect such superposition! That's the whole point of Leggett's paper, the existence of the coherence gap in the Delft/Stony Brook experiments. Did you even READ those papers? It is NOT just MY interpretation of it.

If you disagree, then write a rebuttal to Leggett's paper and to those two experimental paper and tell them that the coherence gap has NOTHING to do with the superposition of the supercurrent flow! Till then, your opinion on here really has zero value.

Zz.

The superposition of the current flowing in the two direction is protected from decoherence. I think the typical decoherence time here is of the order of 10^(-7) seconds or so. This is what makes it detectable. One can use this to make qubits and implement the necessary quantum logic gates to implement quantum computations.


Clearly, there is no way you could do all of this using coins. But that then doesn't mean that the formalism of quantum mechanics, which generically lead to superpositions, is invalid. It is simply that in case of cpoins, the environment will "see" the difference between the two terms in the superposition, i.e. it will evolve differently and thus you'll have a superposition that involves the coin plus environment.

To experimentally prove that this picture is not correct and wavefunctions do really collapse as opposed to the system getting more and more entangled with the rest of the universe, one has to find evidence for non-unitary time evolution. That means that we need experimental results that fail to show effects of superpositions where theory predicts they should be detectable.

The proposed experiment with the mirror in a superposition is exactly such an experiment. If it can be carried out, one can test if Penrose is right and that you have gravitational state reduction or perhaps state reduction due to some other unknown mechanism.

But, lacking any such experimental evidence, I don't see why we have to a priori assume that a non-unitary state reduction really happens.

 

[ZapperZ]

This is getting silly. Since you really want to examine this carefully, let's look at exactly what you said, OK?

I strongly disgree with ZapperZ's denialism by hiding behind what can be directly measured in experiments. It should be clear that you won't be able to detect superpositions involving heads and tails, just like you won't be able to verify that Nature is really time symmetric at the macro level.

Let's tackle the last part. We can't verify that Nature is really time symmetric at the "macro level"? Really? And Nature can be verified to be "symmetric" at the "micro level" instead? You wouldn't go nuts if I show broken time symmetry processes at the micro level then?

Next, "... It should be clear that you won't be able to detect superpositions involving heads and tails..."

That actually, should be the END of the discussion. You are saying you can't detect it, which is something I had ASKED repeatedly. However, you continue with some theoretical argument that such lack of detection somehow is irrelevant. Really? Since when? And this is in addition of you admitting that "... there is no way you could do all of this using coins..." So you can't show it, but you BELIEVE in it! Just listen to yourself!

Lacking any such experimental evidence somehow gives you the license to make the speculation, which is rather strange considering that typically, the lack of experimental evidence means that you CANNOT make such speculation. Lacking the ability to show how such unitary time evolution can be done for coin flipping, AND observing that no kind of superposition effect has EVER been detected in such a system, you chose to believe that it is still valid until it is proven to be false! In other words, there are a gazillion angels on a pinhead until someone shows you that it is false!

I am so done with this weird sense of logic.

Zz.

 

[SW VandeCarr]

Decoherence is a red herring here, as all it will do is make a superposition that is confined to the box to transform into a global superposition.

you won't be able to detect superpositions involving heads and tails, just like you won't be able to verify that Nature is really time symmetric at the macro level.

I don't want to get into the middle of this discussion except to say I don't think a heads/tails superposition is a strong argument. Coin tossing appears to be a chaotic (deterministic) process in that it's extremely sensitive to initial conditions. Snedecor and Cochran give a good example in their textbook "Statistical Methods" (I think they still have it in their latest addition. Mine is fairly old).

Essentially, plot H or T results of trials along the x-axis of an x,y plot starting with the 0th trial at the origin. Add 1 on the y-axis for each sequential toss if heads and subtract 1 if tails. (So for three tosses: 1+1-1: y= 1 etc.) Each set of n trials will have, with increasingly high probability as n grows large, a unique plot. Moreover, the plot will be predominantly above or below the x-axis for a given set. Overall the plots of individual sets will tend to diverge as you would expect in a chaotic process.

 

[Count Iblis]

See my reply here:


https://www.physicsforums.com/showpost.php?p=2241666&postcount=64


You need to have at least some theoretical framework to interpret experimental results, otherwise the experiments are pointless. Then, if you have different theories you can do experiments to decide which one is right. Or you could have a single theory and try to falsify that.


Suppose we have a theory that is not falsified which tells us something about the universe that is difficult to directly verify and in some cases impossible to verify. That difficulty is then consistent with the theory itself. Where it can be verified, it has been verified (otherwise the theory would already been falsified).

Then, lacking well motivated reasons based on physics to doubt the validity of the theory in the regime where we can't verify that aspect of the theory, why would we doubt it?

E.g., why not doubt whether in the interior of Zeta Riticuli, the laws of physics operate as we think it does? Unless there are good theoretical reasons to believe that, the mere lack of direct experimental verification is not a good reason for such doubt.

 

[ZapperZ]

See my reply here:


https://www.physicsforums.com/showpost.php?p=2241666&postcount=64


You need to have at least some theoretical framework to interpret experimental results, otherwise the experiments are pointless. Then, if you have different theories you can do experiments to decide which one is right. Or you could have a single theory and try to falsify that.

Then use a theoretical framework to interpret the result of a coin toss and SHOW ME the effect of superposition!

You will NOTE that I used such theoretical framework as developed by Leggett to interpret the existence of the coherent gap in the SQUID experiment as signifying the presence of superposition of the supercurrent. Now do the SAME for the coin toss.

If you can't, then you've made an empty statement with zero justification.

Zz.

 

[Adrian59]

My last comment was an attempt to get back to the starting question in this thread. However since there still is some debate on the validity of the coin toss, can I suggest a compromise. We all know that a coin is essentially a classical object but since it is extremely difficult to measure all its initial conditions; it behaves like a random event and as such we could accept it as a surrogate marker for one.

The converse is illuminating, since we are accepting as read that QM is inherently random, though it may only be random because we haven’t yet discovered a more fundamental theory. So in effect both events (coins & QM) may be considered random in the absence of a more complete understanding of the underlying mechanics.

Finally, those who don’t like tossing coins can always think of measuring spin whenever coins are mentioned – that’s a pure QM binary event & exhibits superposition. Of course a classical object like a coin won’t exhibit superposition which brings me back to the cat which I, also, do not think will exhibit superposition. The cat is in a multiple decohered state as any large multi-cellular being must be and Schrodinger’s thought experiment is just a very clever way of challenging our belief that QM is probabilistic.

 

[SW VandeCarr]

We all know that a coin is essentially a classical object but since it is extremely difficult to measure all its initial conditions; it behaves like a random event and as such we could accept it as a surrogate marker for one.

I agree with one caveat. Chaos Theory is a classical deterministic theory (with no allowance for superpositions). QM is also deterministic in terms of predicting probabilities. Given our current state of knowledge, QM is the only source of "true" randomness (under strictly calculated probability distributions). No doubt there are a host of classical phenomena which are effectively random for most practical purposes. I don't see why tossing coins should be singled out as having some strange kind of superposition. Coins are, after all, manufactured objects and no two coins are exactly alike.

 

[ArielGenesis]

I am sorry but I think it helps me if I ask the question this way:

Assume that coin tossing is quantum and super position applies.

What should we expected as the result of that assumption?

in other words: beside the absence of evidence, what is the proof that coin tossing is not quantum, while Schrodinger cat is.

 

[SW VandeCarr]

I am sorry but I think it helps me if I ask the question this way:

Assume that coin tossing is quantum and super position applies.

What should we expected as the result of that assumption?

in other words: beside the absence of evidence, what is the proof that coin tossing is not quantum, while Schrodinger cat is.

I would simply say that coins are not quantum "objects". Every electron is exactly like every other electron. Every uranium atom is exactly like every other uranium atom. That's why it's impossible to detect which atom will be observed to decay next and when it will do so. Every U238/U235 atom is assumed in QM to be in a superposition of the lighter and heavier isotope at least until it decays (and actually afterward as well since time is symmetric at the quantum level). That's the weirdness of QM. I've just been converted to the statistical (ensemble) interpretation of QM so I don't worry about this anymore. Suffice to say that coins, while they can in theory be described by a wave function, are not quantum 'objects'. Every coin is unique. (And never ask anyone to prove a negative.)

 

[Count Iblis]

I am sorry but I think it helps me if I ask the question this way:

Assume that coin tossing is quantum and super position applies.

What should we expected as the result of that assumption?

in other words: beside the absence of evidence, what is the proof that coin tossing is not quantum, while Schrodinger cat is.

I think you can't just assume things on an ad hoc basis without precisely defining what it means in a mathematical consistent way. So, you should simply formulate two complete and consistent theories and then see what difference it would make.

That is basically the point I made to ZapperZ, but that didn't come across to him well. So, you can assume that quantum mechanics is always valid, which then leads to macro superpositions that will typically be completely decohered and thus unobservable, except for the very special cases cited by ZapperZ involving SQUIDS.

An alternative model would be some hybrid quantum/classical theory where superpositions, even in a completely decohered form do not exist.

I think that it is difficult to formulate such a consitent theory. But what you could do is do experiments designed to falsify the validity of quantum mechanics in the macro domain, e.g. by doing experioments with SQUIDS and show that the macro superpositions that can be observed in that case, decohere faster than predicted by theory, or try to find some other discrepancy with theory.


Okun explains here:

http://arxiv.org/abs/hep-ph/0505250

what the problem is if you do experiments or try to interpret the results of experiments without a firm and consistent theoretical basis. He examins the case of the charge of the photon and discusses experimental bounds on the charge. His point is that because there is no consistent theory that allows the photon to have a charge, at least no such theory is known as of yet, all claims of the form: "observation X had constrained the charge of the photon to be below Y" are nonsensical statements.


Another case is that of the photon mass, see here:

http://arxiv.org/abs/hep-ph/0306245

People have made claims about observations or experiments ruling out the mass of the photon to be higher that some value. However, as the article points out, such statements are conditional on the theory. The authors come up with a more realistic theory about the photon mass and what do we see: All of the extremely sharp experimental/observational bounds are null and void; we are left with the bound implied with a test of Coulomb's law done somewhere in the early 1970s.


It is for these reasons that I insist on discussing things within a framework of a consistent theory. Since a hybrid quantum/classical theory is inconsistent, at least if you formate it in a naive way by assuming that macro superpositions do not exist, then there is little point in trying to do experiments or think of what experiments you could do rule out such hybrid quantum/classical theories in favor of quantum mechanics being valid on all scales.

This does not mean that there is no point in trying to create macro superpositions in the lab. How exactly quantum theory effectively becomes classical mechanics is not exactly known, so such experiments can probe this. But I don't think it makes sense to question if coin tosses can be in superpositions (that are completely decohered and thus unobservable), unless one can formulate some consistent theory in which superpositions cease to exist.

 

[ZapperZ]

That is still not the complete story.

First of all, the SIZE has nothing to do with all of this. There are every indication to show that "macro"-sized objects can, in fact, exhibit quantum properties. The Delft/Stony Brook experiments involved 10^11 particles exhibiting such properties. We have seen this size gets progressively bigger all the time.

The issue here is how large of a length scale and how long of a time scale can one maintains the coherence of the system. That, to me, is the first and foremost fundamental criteria of observing quantum properties. It is why superconductivity plays a central role in this because no other system can show quantum phenomena in a clearer fashion at a macroscopic scale.

Now, having said that, at what point, and why, do we lose such observation? Decoherence? Sure, but even that isn't sufficient, or at best, incomplete, and this is NOT just from the observational point. It is also from the theoretical standpoint. We have seen that even ONE, single interaction can https://www.physicsforums.com/showpost.php?p=1498616&postcount=55". So it doesn't even require a gazzillion interactions, which would make it even infinitely WORSE to try and model.

But we are also forgetting that our measurement can, in fact, cause the classical properties to arise out of the system. It has been shown that https://www.physicsforums.com/showpost.php?p=1520644&postcount=58" actually can easily be responsible for our classical world!

So there are at least now, two different factors that can easily cause a lot of destruction to any quantum effects, and none of these have ever been carried out theoretically all the way to the coin-tossing phase. Now I have no idea if we can eventually do a quantum description of a coin-tossing. However, my original objection was the naive idea that one can actually write a wavefunction for coin-tossing! That wavefunction was MY objection! To me, that contradicts your latter claim and admission that we cannot carry through such unitary evolution up to the coin-tossing scale. Yet, you had zero qualm in writing such nonsensical wavefunction. To me, when you CAN write such wavefunction then there are observational consequences that can be checked. That was what I ASKED!

The challenge isn't about QM being valid at a large scale. The challenge was your decision that you CAN write THAT particular wavefunction out of thin air.

Zz.

 

[ArielGenesis]

"To me, when you CAN write such wavefunction then there are observational consequences that can be checked."ZapperZ

and what are those observational consequences might be?

 

[Adrian59]

That is still not the complete story.

First of all, the SIZE has nothing to do with all of this. There are every indication to show that "macro"-sized objects can, in fact, exhibit quantum properties. The Delft/Stony Brook experiments involved 10^11 particles exhibiting such properties. We have seen this size gets progressively bigger all the time.

The issue here is how large of a length scale and how long of a time scale can one maintains the coherence of the system. That, to me, is the first and foremost fundamental criteria of observing quantum properties. It is why superconductivity plays a central role in this because no other system can show quantum phenomena in a clearer fashion at a macroscopic scale.

Now, having said that, at what point, and why, do we lose such observation? Decoherence? Sure, but even that isn't sufficient, or at best, incomplete, and this is NOT just from the observational point. It is also from the theoretical standpoint. We have seen that even ONE, single interaction can https://www.physicsforums.com/showpost.php?p=1498616&postcount=55". So it doesn't even require a gazzillion interactions, which would make it even infinitely WORSE to try and model.

Zz.

I agree that size isn't the whole story. Also, all of us will be familiar with the twentieth century version of Young's double slit experiment (I think courtesy of Albert Michelson) when very little interference lost the pure quantum state. It is of note that most of the large scale examples of superposition are in the low temperature arena; SQUIDS & super-conduction (of course the S in the abbreviation SQUID does stand for that). Moreover, if there was no chance of macro scale superposition, that is bad news for quantum computing. However, as has been mentioned already in this thread, thermal agitation is a potent destroyer of the pure quantum state & the cat at 310 K has very little chance (a cat in hell’s chance even) of staying in any pure quantum state.

 

[Count Iblis]

The challenge isn't about QM being valid at a large scale. The challenge was your decision that you CAN write THAT particular wavefunction out of thin air.

It is the most general wavefunction for an isolated system. Of course the assumption that the system can be isolated at all is not realistic. But that doesn't change anything qualitatively, as all you get is an entangled superposition with the rest of the universe.

 

[ZapperZ]

It is the most general wavefunction for an isolated system. Of course the assumption that the system can be isolated at all is not realistic. But that doesn't change anything qualitatively, as all you get is an entangled superposition with the rest of the universe.

You have no justification at all for being able to write a wavefunction that can contain the COMPLETE description of the coin-tossing system. Just because you can write one, doesn't mean that it is appropriate for THAT system. You haven't given any such justification.

Furthermore, such wavefunction should give indications of the existence of such superposition, the same way we detect the coherence gap in the SQUID experiment AND the way we detect bonding-antibonding in chemical bonds. Where are they in YOUR system? This is something I asked for very early on, and something you completely side-stepped. Not only that, you then turned around and somehow admitted that there's no way to carry forth the unitary time evolution of QM into the classical realm of coin-tossing. Yet, this is RIGHT AFTER you had just written the wavefunction for it! To me, these are completely nonsensical and contradictory statements.

And why did it take you THIS long to respond to my last posting. The case has gone very cold!

Zz.

Zz.

 

[ZapperZ]

"To me, when you CAN write such wavefunction then there are observational consequences that can be checked."ZapperZ

and what are those observational consequences might be?

Ask the person who wrote it for this coin-tossing system. I'd like to know as well.

The observational consequences for other quantum systems are well-known : bonding-antibonding, coherence gap in the Delft/Stony Brook experiments, etc.. etc. Read the Leggett paper that I had referred to on here.

Zz.

 

[Hurkyl]

Can you point out to me the effect of superposition on coin tossing?

Have I misunderstood something? Isn't "the effect of superposition on coin tossing" supposed to be "quantum mechanics reproduces classical results"?

The thread partially reads as if you're trying to debunk people claiming that QM can reproduce classical observations by challenging them to show that classical observations aren't reproduced.

 

[ArielGenesis]

ok look sir ZapperZ, i understand you are in this heated debate. but for me who just study the QM at the very surface, none of your 'evidence' (bonding-antibonding, coherence gap in the Delft/Stony Brook experiments) actually help my understanding.

for me to understand the implication of superposition, (a topic which happen to be introduced together with QM even in high school textbooks) I need a simple example that i can understand with ease in my current state of knowledge. I had a wishful thinking that by assuming superposition principle does apply in coin tossing, I can actually understood superposition and thus the essence that make a Schrodinger cat quantum instead of a just another coin tossing.

 

[ZapperZ]

ok look sir ZapperZ, i understand you are in this heated debate. but for me who just study the QM at the very surface, none of your 'evidence' (bonding-antibonding, coherence gap in the Delft/Stony Brook experiments) actually help my understanding.

How was I to know what your level of "understanding" is? You asked, I answered. You are more than welcome to look them up yourself. If you are really just about to study QM at the very surface, then you should also consider that maybe, many of these things will require a bit more background prerequisites for it to sink in. Furthermore, if you do a search on here, I've posted many lengthy explanation on the implication of the Delft/Stony Brook SQUID experiments. So I'm not just throwing things out without making any effort at explaining why and how of the experiments.

And normally, I would, but I'm on vacation right now, and you'll understand why I don't wish to take a lot of time to make lengthy responses, especially when I've done it many times before.

for me to understand the implication of superposition, (a topic which happen to be introduced together with QM even in high school textbooks) I need a simple example that i can understand with ease in my current state of knowledge. I had a wishful thinking that by assuming superposition principle does apply in coin tossing, I can actually understood superposition and thus the essence that make a Schrodinger cat quantum instead of a just another coin tossing.

Unless someone can show me the effect of superposition on coin-tossing, the way we can with quantum systems, then claiming that coin-tossing can be described via QM wavefunction is unverified and unjustified. It is as simple as that.

Zz.

 

[ZapperZ]

Have I misunderstood something? Isn't "the effect of superposition on coin tossing" supposed to be "quantum mechanics reproduces classical results"?

The thread partially reads as if you're trying to debunk people claiming that QM can reproduce classical observations by challenging them to show that classical observations aren't reproduced.

Under SOME conditions, QM can reproduce classical results (eg: harmonic oscillator). However, this is not true in general, and certainly hasn't been shown via First Principles in systems in which there are a gazillion couplings to the environment resulting in purely classical systems. It is why we still have a major debate on the classical-quantum transition. If this is a done deal, why bother with more studies on the mesoscopic scale studies? The Penrose suggestion on superposition with mirrors would have been a waste of time if this issue is settled!

Classical systems looks utterly different than QM systems. It exhibits no superpositions, no anti-correlation, no anti-bunching, etc. How does it gets that way from a starting point of QM description? We have no universal agreement on this issue, even if decoherence is the leading candidate. Do YOU know of any? And do you actually find nothing wrong with that "wavefunction" for coin-tossing, which is the major part of my disagreement in this thread?

Zz.

 

[Hurkyl]

Under SOME conditions, QM can reproduce classical results (eg: harmonic oscillator). However, this is not true in general, and certainly hasn't been shown via First Principles in systems in which there are a gazillion couplings to the environment resulting in purely classical systems.
...
Classical systems looks utterly different than QM systems.

You didn't mean that literally, did you? Is there really an (empirically verified) classical result for which is known that it cannot be reproduced by QM?

I'm going to assume not -- that you just meant that it is just not known whether QM reproduces classical results. However, settling that is a matter of theory not experiment. (put differently, we already have the experimental results for this question)

And do you actually find nothing wrong with that "wavefunction" for coin-tossing

The relative state of the coin-dog system is surely going to be a mixed state, not the pure state that was proposed.

I suppose it's a little optimistic to assume the coin system and the dog system are crisply defined and disjoint, and that all of the states of those systems are cleanly categorizable into head/tail and alive/dead.

But other than that, I confess it looks like the natural conclusion from the hypothesis that quantum mechanics is valid on these scales.

 

[Count Iblis]

Unless someone can show me the effect of superposition on coin-tossing, the way we can with quantum systems, then claiming that coin-tossing can be described via QM wavefunction is unverified and unjustified. It is as simple as that.

How else would you describe it? The wavefunction I wrote down earlier in the thread was in a hypothetical setting where you would be able to keep everything in the box isolated from the environment. But, in general, one can assume that it is entangled with the rest of the universe.

A classical description is ruled out a priori, because classical mechanics is known to be false. Pretending that the generic state does not involve some complicated superposition (involving the coin and the rest of the universe), is very strange.


The effects of any such superposition must be the same as what classical mecanbics predicts, just like General relativity reduces to classical mechanics at weak fields and low speeds. It doesn't mean that at low velocities and weak fields particles do not move along geodesics.

In case of quantum mechanics, the classical limit is a far more complicated issue, one of the reasons being precisely that you do not get rid of global superpositions in the classical limit.

 

[Count Iblis]

Consider a universe containing one or more coins. For one particular coin we can using some convention say that it is in the "tails" or "heads" state. So, there exists an observable A with eigenstates |heads> and |tails>. We can then find a complete set of commuting observables that includes A, for the whole universe. This requires extending A so that the result of an observation of the coin can include the result that the coinn isn't actually there.

This then amounts to expanding the wavefunction in the form:


|psi> = |psi_1>|head> + |psi_2>|tail> + |psi_3>|no coin>

where the |psi_i> contains the information you need in order to specify the state of the universe apart from specifying that the coin is/isn't there and if it is there the head/tail state, so it includes the state of the atoms in the coin as well.

If the initial state is |psi>|head> then under time evolution, the state will evolve to be in some superposition of |head>, |tail>, unless the information present in |psi> yields a zero amplitude for one of the head or tail sectors. One can argue that this is unlikely if the initial state contains a coin thrower who will decide to throw the coin a few days in the future. You would then expect that the exact way he will throw the coin a few days later will not be sharply enough defined for the outcome to be deterministic.

 

[ArielGenesis]

If you are really just about to study QM at the very surface, then you should also consider that maybe, many of these things will require a bit more background prerequisites for it to sink in.

I do consider that and my knowledge will eventually evolve be at that state. But for now I am not and I hope through this forum I could achieve firm basic understanding of the foundational principle of quantum mechanic, such as superposition, with my current technical and mathematical skill.

So far, solving all the pde for 1D quantum system and hydrogen atom and doing that in terms of operators or Hilbert space or matrix have not actually help my basic understanding. Or at least I feel, or as you can see, I am a bit lost in the interpretation.

 

[SW VandeCarr]

I do consider that and my knowledge will eventually evolve be at that state. But for now I am not and I hope through this forum I could achieve firm basic understanding of the foundational principle of quantum mechanic, such as superposition, with my current technical and mathematical skill.

So far, solving all the pde for 1D quantum system and hydrogen atom and doing that in terms of operators or Hilbert space or matrix have not actually help my basic understanding. Or at least I feel, or as you can see, I am a bit lost in the interpretation.

ArielGenesis, no one understands quantum mechanics. Stick with the math which gives numerous predictions that have been tested and never falsified. Forget about trying to understand what it all really means (at least for now). It will drive you crazy. This thread is an example.

 

[ZapperZ]

Consider a universe containing one or more coins. For one particular coin we can using some convention say that it is in the "tails" or "heads" state. So, there exists an observable A with eigenstates |heads> and |tails>. We can then find a complete set of commuting observables that includes A, for the whole universe. This requires extending A so that the result of an observation of the coin can include the result that the coinn isn't actually there.

This then amounts to expanding the wavefunction in the form:


|psi> = |psi_1>|head> + |psi_2>|tail> + |psi_3>|no coin>

where the |psi_i> contains the information you need in order to specify the state of the universe apart from specifying that the coin is/isn't there and if it is there the head/tail state, so it includes the state of the atoms in the coin as well.

If the initial state is |psi>|head> then under time evolution, the state will evolve to be in some superposition of |head>, |tail>, unless the information present in |psi> yields a zero amplitude for one of the head or tail sectors. One can argue that this is unlikely if the initial state contains a coin thrower who will decide to throw the coin a few days in the future. You would then expect that the exact way he will throw the coin a few days later will not be sharply enough defined for the outcome to be deterministic.

Then show the effect of such superposition to VALIDATE that such superpostion exists.

You will note that not only are many measurements that we have validates such superposition, all this rigorous theoretical and experimental verification were done JUST to show the existence of such superposition. In other words, these were not simply accepted just because theory, or someone, says so!

So we know that by looking at the coin itself will NOT tell you that before the act of measurement, the coin was in a superposition of state. Come up with a measurement similar to the coherent gap in the SQUID supercurrent, or the bonding-antibonding in chemical bonds, that clearly show the effect of such superposition. Till then, you wavefuction is a speculation.

Zz.

 

[Count Iblis]

Then show the effect of such superposition to VALIDATE that such superpostion exists.

I think this is an unreasonable demand, because what you are effectively asking is a deviation from classical theory at the macro level which one would not expect to exist, except in exceptional cases.
And the seemingly exceptional case of the flux qubit is actually not as macroscopic as it seems to be, as explained here:

http://arxiv.org/abs/quant-ph/0609007

ZapperZ's demand is a bit like someone making the claim that objects moving under gravity always move along geodesics and not according to a Newtonian gravitational potential, even in cases where gravity is very weak. Then a ZapperZ like sceptic comes along demanding experimental proof for that in the weak gravity limit.

Clearly in the case of general relativity, this would be unreasonable because the idea of a dualistic description of Nature is a priori not seen to be tenable. In case of quantum mechanics, however, this is atitude is different, because quantum mechanics is tradionally formulated as a dualistic theory in which classical concepts play an important role.

But then, this is an effective formulation of a true quantum theory at best. The classical world has to arise from quantum dynamics, the precise way in which that happens is still under discussion. But this lack of understanding does not always preclude one from setting up a general argument, like in this case one that shows that a superposition exists in the macro-world.