Questions About Quantum Theory: What's Wrong?

[caribou]

Isn't "interaction-free measurement" an oxymoron? Can you please construct a QM state that fits into your description above?

Okay, I'm going by the start of Chapter 18 of Robert Griffiths' book Consistent Quantum Theory.

What we have is a particle which goes through a beam-splitter and into two output channels with detectors in each, and the detectors are at different distances along each channel from the beam splitter.

After the beam splitter but before any detector, this particle is in a delocalized state. It's just the usual "particle state" = ("state A" plus "state B") over "the square root of 2".

And then, the more interesting of the two possible series of events is if the channel with the detector which is closer to the beam splitter doesn't have its detector triggered by a certain time, we know the other channel with the detector which is farther from the beam splitter will have its detector triggered at a later time.

So if we don't detect the particle by a certain time in one channel, it must be detected at a later time in the other channel. But that means we went from having a delocalized state to a localized state even though there was no detection and no interaction. So we learned where something is because we "measured" it not by interaction but with simple reasoning from a lack of interaction. The wave function collapsed because nothing happened. Which is strange.

Griffiths says:

While it might seem plausible that an interaction sufficient to trigger a measuring apparatus could somehow localize a particle wave packet somewhere in the vicinity of the apparatus, it is much harder to understand how the same apparatus by not detecting the particle manages to localize it in some region which is very far away.

This second, nonlocal aspect of the collapse picture is particularly troublesome, and has given rise to an extensive discussion on "interaction-free measurements" in which some property of particle of a quantum system can be infered from the fact that it did not interact with a measuring device.

Griffiths also says it would be difficult but not out of the question to do such an experiment. His explanation for the whole strange situation is that the collapse is a useful mathematical shortcut and not a physical effect.

This is not to say, however, that strange concepts all disappear in the conclusions being reached by the physicists whose work I've been relating in this thread.

Decoherent/consistent histories essentially follows Everett's approach but doesn't assume the other "worlds" are real. However, it still has its own peculiarities.

Roland Omnes' book Understanding Quantum Mechanics details a simple "ideal von Neumann experiment" at the start of Chapter 19 which has me going "What?!" myself, as it shows in an experiment quite similar to the "interaction-free" one above how you can basically measure which channel the particle is in but then later recombine the wave packets from both channels and this recombination will destroy the result of the earlier measurement! And this is even with the recombination of the particle's states occurring at any distance from the measuring device!

So we can in principle, using the wave function collapse viewpoint, then go and "uncollapse" the collapsed wave function. From any distance.

In an ideal experiment. In theory.

Omnes says:

This shows the most problematic aspect on an ideal measurement: the data it yields are not obtained once and for all. Apparently lost interferences can be regenerated later in the measuring device by an action on a distant system (the particle). There is no possibility for considering facts as being firmly established. One may see the result as a particularly vicious consequence of EPR correlations or express it by saying that Schrodinger's cat cannot be dead once and for all, because evidence for his survival can always be retrieved.

Thankfully, however, decoherence comes to the rescue in the real world and obliterates this alarming possibility so it has no any meaningful chance of occurring.

So my understanding is of all this is that, in theory, the particle state which didn't occur can come back and haunt the particle state which did occur. We have no wave function collapse and interaction-free measurements anymore but we do have is all the unrealized states smashed up and hidden all over the place.

Maybe I'm wrong but that's what they very much seem to be saying. I can well understand if people want to stick to Copenhagen. It works and works well, just it has a few relatively unimportant conceptual hiccups that are quite understandably ignored by most.

I decided, though, I wanted to read the latest and best research and you see the strange places it's lead me.

 

[dextercioby]

I'm afrain that neither me,nor Zz or Reilly do not share your enthusiasm and concern regarding the fate of the Copenhagen Interpretation of Nonrelativistic Quantum Mechnics.

That doesn't mean your post is not interesting...It is...

Daniel.

 

[ZapperZ]

Okay, I'm going by the start of Chapter 18 of Robert Griffiths' book Consistent Quantum Theory.

What we have is a particle which goes through a beam-splitter and into two output channels with detectors in each, and the detectors are at different distances along each channel from the beam splitter.

After the beam splitter but before any detector, this particle is in a delocalized state. It's just the usual "particle state" = ("state A" plus "state B") over "the square root of 2".

And then, the more interesting of the two possible series of events is if the channel with the detector which is closer to the beam splitter doesn't have its detector triggered by a certain time, we know the other channel with the detector which is farther from the beam splitter will have its detector triggered at a later time.

So if we don't detect the particle by a certain time in one channel, it must be detected at a later time in the other channel. But that means we went from having a delocalized state to a localized state even though there was no detection and no interaction. So we learned where something is because we "measured" it not by interaction but with simple reasoning from a lack of interaction. The wave function collapsed because nothing happened. Which is strange.

Er.. no. I disagree that you made no detection just because you didn't detect anything. It's like saying I have to make a measurement of BOTH entangled pairs to know the state of both particles. I don't. I need to make a measurement of only one. This is because both particles are part of a "macro particle" in which one measurement gives me both info. It is the same with your beam splitter. The issue here isn't the photon. It is the system in which the two detectors are "entangled" via the knowledge of one determing the state of the other. I could have easily done this with a double-slit experiment and put a detector at just one slit. If I know a particle passed through one slit, I do not need to make a determination that it didn't pass through the other.

But then does this mean that QM simply reflects our "state of knowledge" rather than an inherent property of the universe? If this is the case, then a superposition of two states is really a system in which it is in one state OR the other, and not a mixture of BOTH states simultaneously. This will be no different than tossing a coin. I will then reinvoke the Schrodinger Cat-type experiments of H2 molecules and those damn SQUID experiments. Via these experiment, I will say that we DO have evidence to point out that QM does in fact reflect an intrinsic property of nature and NOT just our state of knowledge. So it is not just a mathematical artifact.

Note that QM makes no mention of the mechansim that occurs upon a particular measurment. The "collapsing" wavefunction is purely interpretation, thanks to CI. I have always maintained that one needs to understand and separate out the formalism and the interpretation. This allows the possibility of the "shut up and calculate" school of thought that bypasses, for most part, the tediousness of "interpretation".

Zz.

 

[ZapperZ]

Huh? We can perform imaginary experiments using the theory that we know, which gives us nonsense. We don't need a (real) experiment to tell us that something that has to change.

I disagree. You are discounting emergent phenomena that are entirely possible given the complexity of the situation. That's a distinct possibility that almost everyone ignores. I could tell you precisely the equation of motion of a bunch of gas particles, but there's nothing in that equation that will predict a phase transition and where it will occur. Such observation should caution anyone who thinks all of what we know can be extrapolated without any discontinuities. What if there is such a discontinuity between QM and GR equivalent of such a phase transition? Aren't there already people working on such ideas?

Again, using your criteria of a "direct" experimental evidence, we have none. And if you are convinced that QM and GR can be merged, then I do not see the issue of either of them being "logically inconsistent" in the first place. Or did I "purposely" misread your argument again?

Zz.

 

[Stingray]

I disagree. You are discounting emergent phenomena that are entirely possible given the complexity of the situation. That's a distinct possibility that almost everyone ignores. I could tell you precisely the equation of motion of a bunch of gas particles, but there's nothing in that equation that will predict a phase transition and where it will occur. Such observation should caution anyone who thinks all of what we know can be extrapolated without any discontinuities. What if there is such a discontinuity between QM and GR equivalent of such a phase transition? Aren't there already people working on such ideas?

I completely agree with you. My entire point has been that we can't extrapolate GR and QM into regimes where both "should" be important.

There are actually people working on emergent spacetime and such things. It is certainly a reasonable possibility, although I don't have very much confidence that the theorists working on it right now are likely to succeed without experimental help (some of them disagree).

Again, using your criteria of a "direct" experimental evidence, we have none. And if you are convinced that QM and GR can be merged, then I do not see the issue of either of them being "logically inconsistent" in the first place. Or did I "purposely" misread your argument again?

I said that they can be merged in the sense that there will be a single theory which is everywhere self-consistent and reproduces all experiments that have been attributed to both GR and QM. I was so confident in this statement because it is extremely weak. It basically just says that the universe obeys knowable laws.

In contrast, I said that GR and QM IN THEIR CURRENTLY ACCEPTED FORMS do not go together. Again, I don't think this is a controversial statement.

 

[Eye_in_the_Sky]

reply to post #111

That is a logical interpretation of an axiom.The first axiom.If u reject it,by claiming that the "hidden variables",which are obviously excluded by 1-st principle and by the claim that all one needs to know is an CSCO and solve SE,have "physical existence",then u don't have QM anymore.

I cannot say I understand what you have meant in the above.

Let me nevertheless try to clarify further what I have meant in connection with CSCO's.

Upon completing a ("filtering"-type of) measurement of a CSCO upon a system, the output quantum state is necessarily pure. ... Correct?
... Yes, of course.

Given that, then, the question can still be asked: Does this pure state provide a "complete" characterization of the "real factual situation" pertaining to the system?

If one answers this question in the affirmative, then one is forced to say that "collapse" as it relates to the object (i.e. the system in question) is not the same in a quantum context as it is in a classical context.

On the other hand, if one answers the question in the negative, then one leaves open the possibility that "collapse" with regard to the object can be the same in a quantum context as it is in a classical one. (Note: In such a case there would still have to be more to the state vector than just a "giver of probabilities".)

Now, I must emphasize that what I have said above is no more than part of an attempt to convince Reilly that "collapse" – as it relates to the object – can be said to be the same in quantum mechanics as it is classical mechanics only if one purports the physical existence of "hidden variables".

... And in the end (assuming we have reached it), my suspicion is that Reilly already knew this, but that his intention was to think of "collapse" only as it relates to the subject (i.e. the "knower"). In that case one is free to think of "collapse" as being the same in quantum and classical contexts. However, it would be misleading to say so without making the terms explicit.

-------------------

Iff you have a viable alternative;for 80 yrs one doesn't have that and my opinion is he won't...

Nowhere have I purported that the correct answer is "NO" to a question such as the following:

Does this pure state provide a "complete" characterization of the "real factual situation" pertaining to the system?

(Neither, however, have I anywhere purported that the correct answer is "YES".)

 

[caribou]

The issue here isn't the photon. It is the system in which the two detectors are "entangled" via the knowledge of one determing the state of the other.

I think I know what you mean. When we include the particle and detectors together we arrive sooner or later at a superposition of detection states, collapsing into one or the other possible correlated results as in EPR.

I believe this leads to questions such as what causes the collapse and when does it happen. We could have assigned it to have happened as far back as just after the beam splitter. This possibility seems to agree with wave function collapse being a mathematical rather than physical event and would certainly agree with your suggestion that "the 'collapsing' wavefunction is purely interpretation".

Also, the EPR-like correlation leads to questions about faster-than-light effects.

Of course, the decoherent histories theory I've been relating still has its own question in that if we always have a superposition of detector states, why do we observe one result to have happened and not another. Indeterminism is the escape from that question, I believe.

But then does this mean that QM simply reflects our "state of knowledge" rather than an inherent property of the universe? If this is the case, then a superposition of two states is really a system in which it is in one state OR the other, and not a mixture of BOTH states simultaneously. This will be no different than tossing a coin. I will then reinvoke the Schrodinger Cat-type experiments of H2 molecules and those damn SQUID experiments.

I'd add that Robert Griffiths has pointed out that a macroscopic superposition state can be made up from more than just the states we think of making it up, much like a vector in elementary geometry can be written as more than just the sum of one pair of perpendicular vectors we have chosen.

He then says that whatever we think of making up a Schrodinger cat state, it's not at all obvious that it's an alive cat and a dead cat. It's hard to tell what it means.

Looking into these other states is something I really want to have a look at soon to better understand the "fuzziness" of the basic physics.

 

[Hans de Vries]

And then, the more interesting of the two possible series of events is if the channel with the detector which is closer to the beam splitter doesn't have its detector triggered by a certain time, we know the other channel with the detector which is farther from the beam splitter will have its detector triggered at a later time.

Indeed, this sort of "waveform collapsing" goes on all of the time, not only
at the moment of detection but also at every "non-detection"

Most of the wave function "gets lost" for example when it hits the screen
with the splits. Say it has a 10% chance to make it through the splits.
When the particle doesn't hit the screen we assume that his has gone
through the splits and the wave-function goes to back to 100% again behind
the screen due to unitarity.

We know from molecular modeling that we must assume the particle's charge
to be continuously distributed over the wave function. Would this mean then
that 90% of the charge does instantaneously "collapse" to the paths through
the splits? preferably not of course...


This is why my personal picture (Interpretation) of a single particle
in the (not so empty) vacuum is that of a "cloud" of:

N+1 particles plus N (virtual) anti particles rather then the interpretation
where the particle follows N+1 paths at the same time or (worse) is in
N+1 different worlds at the same time.

It's would now be unclear which particle in the cloud is the N+1'th "real"
particle and which are the N virtual particles. Unitarity is guaranteed
because there's only 1 more particle then there are virtual anti-particles.

The continuous distribution of charge could be easily attributed to the
tiny remaining dipole fields of the virtual particle pairs. The same can be
said for the other attributes which are continuously distributed over the
wave function.

If 90% hits the screen and an N+1'th (real) particle gets through we
presume that the virtual pairs go where "they usually go" and take their
energy with them unused. Like virtual pairs typically do. and thus, there
would be no need for a "collapse of the wave function" type of event.

Again, It's a just a personal picture, but it helps me. More then most of the
others.

Regards, Hans

 

[reilly]

Good discussion indeed. The more I think about it, particulalry in regard to the "no measurement" collapse, I think that the wave function/state vector is a way to represent our knowledge. Because Prob(A)=1-Prob(not A), and with a properly executed experiment a la caribou, we know before hand that if during the measurement window, nothing happens in the B channel, then the particle necessarily is in he other channel. As ZapperZ has noted, there is entanglement, admittedly of a rather peculiar sort. I would tend to term it cognitive entanglement rather than apparatus originated entanglement, because this entanglement is due to fundamental logic of our brain. Whether you agree with me or not, it's clear that there is a collapse(change of knowledge) in the brain if the particle does not show up at B.

One could argue, I suppose, that once the particle does not show up in B, the initial wave function with the superposed states is no longer correct. The lack of result provides a new initial condition for the wave function.

I like this approach because it is consistent with the way we use probability in business, market research in particular. It's highly pragmatic: you don't know until you measure -- null results are allowed. Probability is probability, and ultimately it's in your head -- and don't forget, there are systems described by superpositions of states, as in control theory for example.

As I've mentioned before, this approach is championed by Sir Rudolf Peierls. I feel I'm in good company.

What I'm less sure of are the issues of H2 and SQUIDS. So, I'm off to Google-land. God forbid I should have to change my mind.

And to Eye In The Sky -- collapse in the subject indeed. Funny and funky changes in the object leave me feeling very uncomfortable.

And, by the way, we are now having the type of discussion I had hoped we would. Thank you.

Regards, Reilly

 

[ZapperZ]

Also, the EPR-like correlation leads to questions about faster-than-light effects.

But is this really the case? There's nothing that "travels" from one location to another, so how could this be "faster" than light? Furthermore, at no instant are people like Zeilinger claiming that such a scheme can send info faster than light. You STILL need to create pairs of entangled particles and then send them to far away locations. This can never be faster than c.

I'd add that Robert Griffiths has pointed out that a macroscopic superposition state can be made up from more than just the states we think of making it up, much like a vector in elementary geometry can be written as more than just the sum of one pair of perpendicular vectors we have chosen.

He then says that whatever we think of making up a Schrodinger cat state, it's not at all obvious that it's an alive cat and a dead cat. It's hard to tell what it means.

Looking into these other states is something I really want to have a look at soon to better understand the "fuzziness" of the basic physics.

But we can make an observation that would not disturb a particular superposition if there is a non-commuting observable. That's the whole point of the energy gap in the bonding-antibonding bands of H2 molecule and the energy gap in the SQUIDs experiments. By measuring the energy state (which does not commute with the position observable of the electron in an H2 molecule, and also does not commute with the current state of a superfluid across a Josephson junction), we can maintain those superposition and measure the CONSEQUENCES of such superposition. And a consequence of such superposition is just such energy gap! Without such superposition, this energy gap would not be present. This is the clearest indication, at least to me, that such a concept isn't just mumbo-jumbo. It has no classical counterpart, meaning it isn't this OR that, but rather this AND that, and in varying proportions.

So if there is an observable that does not commute with the dead-alive observable of the cat, that's the thing we should measure to detect such superposition. Of course, you have to maintain quantum coherence throughout the whole source+cat+box+etc. for such effects to be measured.

Zz.

 

[vanesch]

Well, here's where we differ. I can't tell if, even if we buy into CI, that we have a "logical inconsistency" or simply it offends our "tastes"!

No, the way CI is formulated, it is a genuine inconsistency, in the sense that Jack and Joe can apply the rules of the game in equally accepted ways, and arrive at different conclusions.
For instance, Joe can claim that a "click in a photodetector" is a measurement, and apply "collapse of the wavefunction", while Jack, slightly more sophisticated, working in solid-state physics, works out the Hamiltonian of the photocathode and EM field and evolves the wavefunction with his hamiltonian of his photodetector.

Jack and Joe now have DIFFERENT wavefunctions: Joe has ONE (randomly selected, following Born's rule) component of a wavefunction Jack has calculated completely and deterministically. Although it will be difficult, Jack could think of interference experiments between the different components of his wavefunction while Joe doesn't: his wavefunction "collapsed".
As long as CI leaves in the dark WHAT is a "measurement" and when can we (in principle) write down a hamiltonian, we have an inconsistent theory in principle (according to the meaning of the word in logic). This is not a matter of taste.

But I know of course (thanks to decoherence) that this doesn't matter, for the time being and the near future, in practice, because obtaining these interferences Jack could in principle obtain, is damn hard.

That's why you can happily work with collapsing (or not) wavefunctions, use Born's rule at will, in the large majority of cases it won't make a bloody difference, and in those cases where it could, the experiments are too difficult... except that progress is made and maybe one day we can do interference experiments with cats, and even with humans :-)

cheers,
Patrick

 

[Hans de Vries]

That's why you can happily work with collapsing (or not) wavefunctions, use Born's rule at will, in the large majority of cases it won't make a bloody difference, and in those cases where it could, the experiments are too difficult... except that progress is made and maybe one day we can do interference experiments with cats, and even with humans :-)

Hmm, I guess it's the extreme level of abstraction that leads to such
preposterous interference extrapolations. All physics and geometry gets
abstracted out.

A buckyball goes through 10¹⁵ phase changes when it travels it's own
length during the experiments. (according to E=hf) It still goes through 10⁹
phase changes when it travels the distance of a single nucleon (10^-15 m)
That is "two" buckyballs have to overlap with an accuracy of 10^-9 of the
size of a nucleus to be interfered out. And this with 70 atoms all vibrating
at 900 K coming out of an oven...

It's often forgotten that the deBroglie phase "travels" with c²/v which
goes to infinity if the speeds goes to zero. To interfere it is not only
necessary to be at the right place but it has also to be at exactly the
right time.



Regards, Hans.


(c²/v is easily shown: if the speed goes to zero then λ goes to infinity.
The frequency however continuous to be f = E₀/h = m₀c²/h.
The speed = fλ = c²/v).

 

[seratend]

For instance, Joe can claim that a "click in a photodetector" is a measurement, and apply "collapse of the wavefunction", while Jack, slightly more sophisticated, working in solid-state physics, works out the Hamiltonian of the photocathode and EM field and evolves the wavefunction with his hamiltonian of his photodetector.

The CI deals only with logical statements and no logical inconsistency is embedded in this formulation (only additionnal intepretations may lead to inconsystencies)
In your example, if Joe is true (the result of his measure is A for the associated observable), Jack has the collapsed updated wave function of Jack. And vice versa. That's all.
The fact that Joe does not measure really the observable he assumes is outside the scope of the problem. It is equivalent to say that jack is wrong when he claims he has the result measurement A of his supposed observable (either the result or the observable is wrong).
CI interpretation just states that when a measurement gives a result A (the result A is true), the wavefunction is collapsed into |A>. The collapse itself is not explained by the CI (as I "interpret" it, it is not very different from the "shut up and calculate").

Seratend.

 

[ZapperZ]

No, the way CI is formulated, it is a genuine inconsistency, in the sense that Jack and Joe can apply the rules of the game in equally accepted ways, and arrive at different conclusions.
For instance, Joe can claim that a "click in a photodetector" is a measurement, and apply "collapse of the wavefunction", while Jack, slightly more sophisticated, working in solid-state physics, works out the Hamiltonian of the photocathode and EM field and evolves the wavefunction with his hamiltonian of his photodetector.

Jack and Joe now have DIFFERENT wavefunctions: Joe has ONE (randomly selected, following Born's rule) component of a wavefunction Jack has calculated completely and deterministically. Although it will be difficult, Jack could think of interference experiments between the different components of his wavefunction while Joe doesn't: his wavefunction "collapsed".
As long as CI leaves in the dark WHAT is a "measurement" and when can we (in principle) write down a hamiltonian, we have an inconsistent theory in principle (according to the meaning of the word in logic). This is not a matter of taste.

But I know of course (thanks to decoherence) that this doesn't matter, for the time being and the near future, in practice, because obtaining these interferences Jack could in principle obtain, is damn hard.

That's why you can happily work with collapsing (or not) wavefunctions, use Born's rule at will, in the large majority of cases it won't make a bloody difference, and in those cases where it could, the experiments are too difficult... except that progress is made and maybe one day we can do interference experiments with cats, and even with humans :-)

cheers,
Patrick

Well then, you should expect what's coming next from 10 miles away... show me an experimental observation that differentiate what Jack and Joe get. If they both end up with different and incompatible reality, then you should be able to predict different results depending on how you approach things.

Zz.

 

[seratend]

Well then, you should expect what's coming next from 10 miles away... show me an experimental observation that differentiate what Jack and Joe get. If they both end up with different and incompatible reality, then you should be able to predict different results depending on how you approach things.
Zz.

Yes, very easy .
Just take 2 voltmeters: an old one (analogic, bought in a super market) (Joe) with a low impedance and the last new one (10 digits digital, HP) (jack) with a huge internal impedance and a third observer (john) that notes the results of joe and jack.
Both (joe and jack) they measure at the same time a non ideal current source. They get different results as noticed by john. So, where is the reality, if there is one?

Seratend.

 

[ZapperZ]

Yes, very easy .
Just take 2 voltmeters: an old one (analogic, bought in a super market) (Joe) with a low impedance and the last new one (10 digits digital, HP) (jack) with a huge internal impedance and a third observer (john) that notes the results of joe and jack.
Both (joe and jack) they measure at the same time a non ideal current source. They get different results as noticed by john. So, where is the reality, if there is one?

Seratend.

So you're expecting that two instruments with different level of accuracy (and function) should give the same identical answer? How is this identical to what vanesch described?

Zz.

 

[seratend]

So you're expecting that two instruments with different level of accuracy (and function) should give the same identical answer? How is this identical to what vanesch described?

Zz.

No almost surely different answers. As vanesh says:

No, the way CI is formulated, it is a genuine inconsistency, in the sense that Jack and Joe can apply the rules of the game in equally accepted ways, and arrive at different conclusions.

We can build an experiment (no need to go to an expensive QM experiment) where we get different and incompatible answers depending on the [possibily false] assumptions we have on the real measurements.

But surely I do not understand well what you want to say (to what part of the vanesh's post your previous post applies)?
(anyway, if you want the same answer, you always have the possibility -small probability - that the voltmeters may give the same answer, if joe is lucky with the current source and the offset error of its bad voltmeter).

However, this does not change the fact that CI is logically consistent. It just tries to underline the possibly false interpretations we can do.

Seratend.

 

[ZapperZ]

No almost surely different answers. As vanesh says:



We can build an experiment (no need to go to an expensive QM experiment) where we get different and incompatible answers depending on the [possibily false] assumptions we have on the real measurements.

But surely I do not understand well what you want to say (to what part of the vanesh's post your previous post applies)?
(anyway, if you want the same answer, you always have the possibility -small probability - that the voltmeters may give the same answer, if joe is lucky with the current source and the offset error of its bad voltmeter).

However, this does not change the fact that CI is logically consistent. It just tries to underline the possibly false interpretations we can do.

Seratend.

Oh, I get it.

I thought you were trying to use your example to illustrate venesh's point of "genuine inconsistency". In your example, there isn't one since one CAN explain why the results are different. This is very much like measuring different times in SR. Yet, we know why they should be different since we can explain them. This isn't a "genuine inconsistency".

To me, genuine or logical inconsistency is like when we shift our coordinate system and the outcome gives completely different description. Nature shouldn't care when we do something that superficial.

Zz.

 

[reilly]

Seratend -- I'm a bit confused by Jack and Joe. What is it exactly that they are doing, what are they measuring? Apparently they are getting different answers when they should not, and I don't get it.

ZapperZ -- The SQUID experiment is, to say the least, disarming, and, like WOW. I've got a bunch of quesions, and have not found a good reference on GOOGLE. Any suggestions?

How "strong" is the barrier? That is, a bound state wave function, I presume, will be non-zero in both current channels. Is there anything like optical pumping and inverted levels? I'm not quite sure about the sequence of events - is one channel empty at the start?

Thanks, and regards,
Reilly

 

[ZapperZ]

ZapperZ -- The SQUID experiment is, to say the least, disarming, and, like WOW. I've got a bunch of quesions, and have not found a good reference on GOOGLE. Any suggestions?

How "strong" is the barrier? That is, a bound state wave function, I presume, will be non-zero in both current channels. Is there anything like optical pumping and inverted levels? I'm not quite sure about the sequence of events - is one channel empty at the start?

Thanks, and regards,
Reilly

OK, why don't I give you the exact citations of all the relevant papers and see if can answer your questions? I'm thinking that I should also put this up in my Journal since I have had to refer to them quite often on here.

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).

This paper clearly outlines the so-called "measurement problem" with regards to the Schrodinger Cat-type measurements.

Zz.

 

[Hans de Vries]

C.H. van der Wal et al., Science v.290, p.773 (2000).
Zz.

This one is online here:

http://qt.tn.tudelft.nl/publi/2001/wal_science2000.pdf

and related papers:

More from Delft


Regards, Hans

 

[seratend]

Seratend -- I'm a bit confused by Jack and Joe. What is it exactly that they are doing, what are they measuring? Apparently they are getting different answers when they should not, and I don't get it.

Reilly

Well, my purpose is to underline (simply) the eternal problem of the interpretation in physics (the connection between the results of the theory and the "real" world).

Jack and Joe are just measuring a voltage of the current source in my basic example. However, a current source may be modeled, as a voltage source with a huge resistance in series. Therefore the two voltmeters give surely a different voltage measure (i.e we apply the well know voltage division: R1/(R1+R2) to get the measured voltage).
Therefore, if Jack and Joe say (interpretation) that they both measure the voltage of the current source, they will get different results (interpretation inconsistency).

Seratend.

 

[vanesch]

The CI deals only with logical statements and no logical inconsistency is embedded in this formulation (only additionnal intepretations may lead to inconsystencies)
In your example, if Joe is true (the result of his measure is A for the associated observable), Jack has the collapsed updated wave function of Jack. And vice versa. That's all.

Why ? In CI, you can CALL a photodetector a measurement apparatus, and then you should think like Joe (and collapse your wavefunction), but you are also free to consider it to be a system under study, and then you can write out its hamiltonian and evolve unitarily. This is what Jack does. NO CHANGE IN THE SETUP IS ASSUMED.

So why do we have "an outcome" in the case of Joe, and do we have "a physical system in evolution" in the case of Jack ?

The fact that CI remains very vague on when to apply process 1 and when to apply process 2, and that in many cases you can do both, according to your own taste (just as you can choose to work in cylindrical or cartesian coordinates), and that THE OUTCOMES ARE INCOMPATIBLE, sounds to me like an internal inconsistency.

The fact that Joe does not measure really the observable he assumes is outside the scope of the problem. It is equivalent to say that jack is wrong when he claims he has the result measurement A of his supposed observable (either the result or the observable is wrong).
CI interpretation just states that when a measurement gives a result A (the result A is true), the wavefunction is collapsed into |A>. The collapse itself is not explained by the CI (as I "interpret" it, it is not very different from the "shut up and calculate").

Yes, but you now simply changed the semantics: what used to be "a measurement" and a "process" is now changed into "having a result" or "not having a result". But that doesn't do away with the difficulty.

As Zzapper asked me, show me the relevant experimental results that make the difference, that's silly of course, there aren't any in the foreseeable future because decoherence makes it hard to do so.
But the very fact that saying that a photodetector is a measurement apparatus or saying that a photodetector is a physical system under study, makes you obtain DIFFERENT states (the former one is a statistical mixture, the latter is a pure state), means that it is IN PRINCIPLE (though it will be hard in practice) possible to do a (second?) "measurement", in an incompatible basis, on the system, and obtain different results (statistical mixtures and pure states give different results in a basis where the density matrix is not diagonal).
The very fact that this is IN PRINCIPLE possible (having two different predictions of outcomes), and that we have two ways of talking about the situation (just by CALLING a photodetector either a measurement apparatus, or a physical system under study, both equally allowable in CI), means to me that the system is logically inconsistent, even though for the time being, this inconsistency will not become visible in an experiment and hence that we can still use the machinery FAPP without any worry.

cheers,
Patrick.

 

[ZapperZ]

Why ? In CI, you can CALL a photodetector a measurement apparatus, and then you should think like Joe (and collapse your wavefunction), but you are also free to consider it to be a system under study, and then you can write out its hamiltonian and evolve unitarily. This is what Jack does. NO CHANGE IN THE SETUP IS ASSUMED.

So why do we have "an outcome" in the case of Joe, and do we have "a physical system in evolution" in the case of Jack ?

The fact that CI remains very vague on when to apply process 1 and when to apply process 2, and that in many cases you can do both, according to your own taste (just as you can choose to work in cylindrical or cartesian coordinates), and that THE OUTCOMES ARE INCOMPATIBLE, sounds to me like an internal inconsistency.

I disagree. I still do not see how the two cases you mentioned are the identical situations and should produce the identical results even via QM.

Yes, but you now simply changed the semantics: what used to be "a measurement" and a "process" is now changed into "having a result" or "not having a result". But that doesn't do away with the difficulty.

As Zzapper asked me, show me the relevant experimental results that make the difference, that's silly of course, there aren't any in the foreseeable future because decoherence makes it hard to do so.

It's not that silly. As I have said before, and as Carver Mead has said in that PNAS paper, we can use superconductivity. It is the clearest manifestation of QM effects, especially coherence, with very strong "quantum protectorate" regime that is immune to many external interactions. So use this and tell me what kind of measurement do you expect to be "different" between the two cases you mentioned.

Zz.

 

[seratend]

Why ? In CI, you can CALL a photodetector a measurement apparatus, and then you should think like Joe (and collapse your wavefunction), but you are also free to consider it to be a system under study, and then you can write out its hamiltonian and evolve unitarily. This is what Jack does. NO CHANGE IN THE SETUP IS ASSUMED.
.

Yes, but you seem to assume that the results of Joe and Jack may be inconsistent that is not possible under CI. As you know, unitary evolution preserves the orthogonality of the vectors (same stuff used in e.g. MWI, MMI etc..). Therefore if the result of a given measurement is true, only a part of the vector, before measurement, should be assumed under the unitary evolution to make other logical assertions on further measurements (the other part "is wrong" simply because the result of the measurement is true: formal logic).

CI does not say what is the "interpretation" of a collapse, just that "abstract measurements" on a system follows this rule. Do not forget that CI formalism does not say how we can realize a "real" ideal measurement, just how to use logical statements (the result of a measure is true) with abstract measurements.
After, an external additional interpretation may say more than what CI says, but it outside the consistency scope of CI.

So why do we have "an outcome" in the case of Joe, and do we have "a physical system in evolution" in the case of Jack ?

No, in CI Joe and Jack just assert that a given outcome is true and not that a system evolves under unitary evolution or not. In other words, Joe and Jack only exist as the logical statement result of the measurements, while the system keeps its unitary evolution. It is always external assumptions that say more than that.
I just recall what CI says with my words: A system is on the collapsed state just after the abstract measurement result is true. That's all.

The fact that CI remains very vague on when to apply process 1 and when to apply process 2, and that in many cases you can do both, according to your own taste (just as you can choose to work in cylindrical or cartesian coordinates), and that THE OUTCOMES ARE INCOMPATIBLE, sounds to me like an internal inconsistency.

Because CI does not intend to describe more (it is not its purpose to describe how the abstract measurements are realized). This resembles somewhat to recurring problem in PF of the paths of quantum particles. QM and CI does not say that particles have a path, just that we can measure the presence of a particle at a given position (the measure result statement). We usually have a classical and a deterministic bias in our way of thinking (surely due to our education) and we must take care in not adding more features to a given formalism (source of inconsistencies) due to this bias.

Yes, but you now simply changed the semantics: what used to be "a measurement" and a "process" is now changed into "having a result" or "not having a result". But that doesn't do away with the difficulty.

That is the heart of the external interpretation you seem to add to the CI. CI does not say what is a measurement. Just that this abstract object allows one to make logical assertions on the system and therefore compute probabilities and system evolutions. [/QUOTE]

Once I say I have a measurement, I have a result (I have a true property: i.e. one of the values of the observable). CI does not say how to activate/deactivate a measurement (no signification in this formalism). There is no time in the collapse, just a causal statement (e.g. like y=f(x) i.e. if x and f are true, then y is true). Therefore “not having a result” only means having another result of the measurement.

You have to understand the “a real photodetector” is not a genuine CI measurement apparatus, just an approximation that gives an approximated result.
Therefore, you have the right to construct “a measurement apparatus” that does not follow the CI results. I gave one such example (the voltmeters).
CI interpretation does not say that a huge system with an infinite (or huge) number of particles is a measurement apparatus, just “a system is on the collapsed state just after the result of the measure is A (i.e. A is true)”.
However, decoherence studies how a huge system may give results analog to the abstract measurement apparatuses of CI.
Note that I am already biased when I say “measurement apparatus” as I think CI deals only with measurements, results and collapse, i.e. it is already a causal bias analysis: what causes the results of a measurement? Answer “the measurement apparatus”. I am already out of the scope of core of CI.

Seratend.

 

[ZapperZ]

I disagree. You are discounting emergent phenomena that are entirely possible given the complexity of the situation. That's a distinct possibility that almost everyone ignores. I could tell you precisely the equation of motion of a bunch of gas particles, but there's nothing in that equation that will predict a phase transition and where it will occur. Such observation should caution anyone who thinks all of what we know can be extrapolated without any discontinuities. What if there is such a discontinuity between QM and GR equivalent of such a phase transition? Aren't there already people working on such ideas?

Zz.

Just to prove that I'm not making this up as I go along, read this...

http://www.nature.com/news/2005/050328/full/050328-8.html

Note that I'm NOT endorsing this. I just want to point out that when you deal with something having this type of degree of certainty, a LOT of things are still up in the air.

Zz.

 

[vanesch]

Yes, but you seem to assume that the results of Joe and Jack may be inconsistent that is not possible under CI. As you know, unitary evolution preserves the orthogonality of the vectors (same stuff used in e.g. MWI, MMI etc..). Therefore if the result of a given measurement is true, only a part of the vector, before measurement, should be assumed under the unitary evolution to make other logical assertions on further measurements (the other part "is wrong" simply because the result of the measurement is true: formal logic).

This is correct of course ; but such a statement is closer to MWI or relative-state views (to which I adhere more) than CI, which I thought, claimed a genuine, irreversible collapse of the wavefunction.

But what you claim is very true: IF the result of a measurement is known to be A, THEN for all matters WE CAN PRETEND THAT the system is in the projected state corresponding to the result A as in CI. But that is, I would say, almost the definition of a relative-state interpretation, and NOT CI.
We have shifted now the concept of what is a measurement into the phrase "the result of a measurement is known to be".

But you could, in principle, do experiments where some "observer" (be it a human being or just a small "measuring device") first "learns about a result" (but it is a different result in each of the different branches!) and then "interferes with itself" where in the process of course he forgot about "the" result because all the different branches of the observer states which had different results come together again (our language is not well-adapted to these situations).
This is thinkable in the case of Jack, but it is NOT in the case of Joe, because in that case, if we consider Joe to do a "measurement" there is a definite result and a definite collapse, and no interference with the other branches is possible anymore.
Embryonic experiments of this kind are delayed-choice quantum erasure experiments ; but you can hardly talk of a photon as a measurement device. However, if we could do the same thing, but this time with little photocells and integrated computers and memory instead of with photons, we would already be a bit further on the path.
If we could make such "microscopic photocells with integrated computer", and they record the "which path" information, but afterwards we make them interfere as to find out the "which interference pattern" information, then at a certain point, the computer "knew" the which path information, but was itself in a superposition of "I know it is the left path" and "I know it is the right path". Then, by making the two branches interfere, it wouldn't know anymore "which path" but you could now extract the "which interference pattern" information.
So from the point of view of the computer, a "measurement" was made, but the wavefunction didn't "collapse" ; it is only that the measurement gave different results for the different branches of the state of the computer (in a typical relative-state interpretation!). By making these different branches interfere again, the notion of "result of measurement" lost its meaning.
But it is difficult as of now to make such microscopic devices interfere in 2-slit experiments or the like. How many atoms do you need to make such a thing (probably a large bio-molecule) ? 10000 ? 100000 ? Buckyballs DO interfere with 70 atoms...

However, to come back to what you said: IF you say that the result of the measurement is A THEN WE CAN PRETEND that the state is the collapsed state corresponding to A, is a very true statement. According to what I understood of CI, it is absolutely not what CI pretends, but then I might have missed what CI actually says. To me, the above statement is the essential content of relative-state interpretations.


cheers,
Patrick.

 

[vanesch]

Just to prove that I'm not making this up as I go along, read this...

http://www.nature.com/news/2005/050328/full/050328-8.html

Note that I'm NOT endorsing this. I just want to point out that when you deal with something having this type of degree of certainty, a LOT of things are still up in the air.

If your point is that there is still a lot to discover and that we are far to know all about gravity and so on, that's of course granted
However, I have to say that I find the article "highly speculative", in an "original thinker" trademark style. Indeed, whenever people say that "future historians of science will wonder how it came that MyDiscovery-TM which is so obvious, took so long to be seen" or something of the kind, I get suspicious

cheers,
Patrick.

 

[seratend]

However, to come back to what you said: IF you say that the result of the measurement is A THEN WE CAN PRETEND that the state is the collapsed state corresponding to A, is a very true statement. According to what I understood of CI, it is absolutely not what CI pretends, but then I might have missed what CI actually says. To me, the above statement is the essential content of relative-state interpretations.
cheers,
Patrick.

Well, in the Messiah QM introduction book 1959 (for the 1st or 2nd edition), I consider as a CI interpretation book, we just have the collapse postulate of the ideal measurement written closely to my previous post. I.e. you *should* view it as a simple mathematical statement ("disconnected" from the physical reality). There is no "we can pretend" (interpretation) in this postulate, just the state of the system in the collapsed state corresponding to A. The collapsed word in this context only means the projection of the state (i.e. |A>= P|psi> is true). It is how I interpret the CI formalism (therefore I may be wrong for the interpretation).
I know, there are many papers on the flavours of CI (I like to call the interpretation of the Copenhagen interpretation ;). However, if we remove the extra words in order to focus on the logical statements of CI we get the following words: ideal measurement, collapse, result, before and after (may be there are some others words ;). The main danger with these words is to attach a meaning that does not exist in the CI (what physicist like to do), i.e. interpreting these words outside the CI formalism (therefore adding extra signification).

Again in your example of "microscopic photocells with integrated computer", (if we assume that a photocell allows an ideal measurement) your measurement apparatuses are there (there is no notion of time - logical statement). CI does not say if you do not look at the result, the result does not exist (no meaning in CI) and that the wavefunction is not collapsed. Just that the result of a measurement "collapses" the wave function in that result state (i.e. we need a measurement). Therefore in your experiment you have a global measurement apparatus made of independent unit measurement apparatuses. Therefore, you need to know all the results of the microscopic photocells to know the new wavefunction "after" the measurement.

CI is a very minimalist set in QM theory and I think it may handle (subset) most of the other interpretations of QM (yours MWI or relative state views or your own mind selection). (I have had a long time to remove all the external incoherent meanings of CI that my professors taught me in my first QM courses a long time ago ;). Now I just take CI for what I think it is: just a consistent basic math tool that connects experimental results to the theory predictions. It is not sufficient (How to realize a real ideal measurement?), but it is a good basis.

For a small analysis on the possible connections between the different interpretations of QM (and to see, a little how CI lives in some of these interpretations), I recommend the text:
Do we really understand quantum mechanics?, F. Laloe, 2002, Quant-ph/0209123 (section 4: historical perspective and section 6: various interpretations). The author sometimes underlines the link between the different interpretations.

Seratend.

 

[seratend]

Well, my purpose is to underline (simply) the eternal problem of the interpretation in physics (the connection between the results of the theory and the "real" world).

Jack and Joe are just measuring a voltage of the current source in my basic example. However, a current source may be modeled, as a voltage source with a huge resistance in series. Therefore the two voltmeters give surely a different voltage measure (i.e we apply the well know voltage division: R1/(R1+R2) to get the measured voltage).
Therefore, if Jack and Joe say (interpretation) that they both measure the voltage of the current source, they will get different results (interpretation inconsistency).

Seratend.

I must add some corrections to my simple low cost experiment (I have made some implicit assumptions ).
* If both joe and jack measures the voltage of the current source (we suppose that the precision of the voltmeters are the same and not the internal resistance), they sureley get both the same result.
* If they measure at different times (one measurement is true at a time), they surely get different results
What is the real voltage of the non perfect current source? (does this sentence alone have a meaning?)

Even if this example is not a real QM one, i think it underlines perfectly most of the problem in QM measurements.

Seratend.